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Academic literature on the topic 'THEORY OF SIGNED GRAPHS'

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Published: 11 September 2023

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Journal articles on the topic "THEORY OF SIGNED GRAPHS"

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Hou, Yaoping, and Dijian Wang. "Laplacian integral subcubic signed graphs." Electronic Journal of Linear Algebra 37 (February 26, 2021): 163–76. http://dx.doi.org/10.13001/ela.2021.5699.

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A (signed) graph is called Laplacian integral if all eigenvalues of its Laplacian matrix are integers. In this paper, we determine all connected Laplacian integral signed graphs of maximum degree 3; among these signed graphs,there are two classes of Laplacian integral signed graphs, one contains 4 infinite families of signed graphs and another contains 29 individual signed graphs.

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Belardo, Francesco, and Maurizio Brunetti. "Connected signed graphs L-cospectral to signed ∞-graphs." Linear and Multilinear Algebra 67, no. 12 (July 9, 2018): 2410–26. http://dx.doi.org/10.1080/03081087.2018.1494122.

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Li, Yu, Meng Qu, Jian Tang, and Yi Chang. "Signed Laplacian Graph Neural Networks." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 4 (June 26, 2023): 4444–52. http://dx.doi.org/10.1609/aaai.v37i4.25565.

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This paper studies learning meaningful node representations for signed graphs, where both positive and negative links exist. This problem has been widely studied by meticulously designing expressive signed graph neural networks, as well as capturing the structural information of the signed graph through traditional structure decomposition methods, e.g., spectral graph theory. In this paper, we propose a novel signed graph representation learning framework, called Signed Laplacian Graph Neural Network (SLGNN), which combines the advantages of both. Specifically, based on spectral graph theory and graph signal processing, we first design different low-pass and high-pass graph convolution filters to extract low-frequency and high-frequency information on positive and negative links, respectively, and then combine them into a unified message passing framework. To effectively model signed graphs, we further propose a self-gating mechanism to estimate the impacts of low-frequency and high-frequency information during message passing. We mathematically establish the relationship between the aggregation process in SLGNN and signed Laplacian regularization in signed graphs, and theoretically analyze the expressiveness of SLGNN. Experimental results demonstrate that SLGNN outperforms various competitive baselines and achieves state-of-the-art performance.

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Zhang, Xianhang, Hanchen Wang, Jianke Yu, Chen Chen, Xiaoyang Wang, and Wenjie Zhang. "Polarity-based graph neural network for sign prediction in signed bipartite graphs." World Wide Web 25, no. 2 (February 16, 2022): 471–87. http://dx.doi.org/10.1007/s11280-022-01015-4.

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AbstractAs a fundamental data structure, graphs are ubiquitous in various applications. Among all types of graphs, signed bipartite graphs contain complex structures with positive and negative links as well as bipartite settings, on which conventional graph analysis algorithms are no longer applicable. Previous works mainly focus on unipartite signed graphs or unsigned bipartite graphs separately. Several models are proposed for applications on the signed bipartite graphs by utilizing the heuristic structural information. However, these methods have limited capability to fully capture the information hidden in such graphs. In this paper, we propose the first graph neural network on signed bipartite graphs, namely Polarity-based Graph Convolutional Network (PbGCN), for sign prediction task with the help of balance theory. We introduce the novel polarity attribute to signed bipartite graphs, based on which we construct one-mode projection graphs to allow the GNNs to aggregate information between the same type nodes. Extensive experiments on five datasets demonstrate the effectiveness of our proposed techniques.

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Tupper, Melissa, and Jacob A. White. "Online list coloring for signed graphs." Algebra and Discrete Mathematics 33, no. 2 (2022): 151–72. http://dx.doi.org/10.12958/adm1806.

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We generalize the notion of online list coloring to signed graphs. We define the online list chromatic number of a signed graph, and prove a generalization of Brooks' Theorem. We also give necessary and sufficient conditions for a signed graph to be degree paintable, or degree choosable. Finally, we classify the 2-list-colorable and 2-list-paintable signed graphs.

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DIAO, Y., G. HETYEI, and K. HINSON. "TUTTE POLYNOMIALS OF TENSOR PRODUCTS OF SIGNED GRAPHS AND THEIR APPLICATIONS IN KNOT THEORY." Journal of Knot Theory and Its Ramifications 18, no. 05 (May 2009): 561–89. http://dx.doi.org/10.1142/s0218216509007075.

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It is well-known that the Jones polynomial of an alternating knot is closely related to the Tutte polynomial of a special graph obtained from a regular projection of the knot. Relying on the results of Bollobás and Riordan, we introduce a generalization of Kauffman's Tutte polynomial of signed graphs for which describing the effect of taking a signed tensor product of signed graphs is very simple. We show that this Tutte polynomial of a signed tensor product of signed graphs may be expressed in terms of the Tutte polynomials of the original signed graphs by using a simple substitution rule. Our result enables us to compute the Jones polynomials of some large non-alternating knots. The combinatorics used to prove our main result is similar to Tutte's original way of counting "activities" and specializes to a new, perhaps simpler proof of the known formulas for the ordinary Tutte polynomial of the tensor product of unsigned graphs or matroids.

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Hameed, Shahul K., T. V. Shijin, P. Soorya, K. A. Germina, and Thomas Zaslavsky. "Signed distance in signed graphs." Linear Algebra and its Applications 608 (January 2021): 236–47. http://dx.doi.org/10.1016/j.laa.2020.08.024.

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Acharya, B. D. "Signed intersection graphs." Journal of Discrete Mathematical Sciences and Cryptography 13, no. 6 (December 2010): 553–69. http://dx.doi.org/10.1080/09720529.2010.10698314.

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Li, Shu, and Jianfeng Wang. "Yet More Elementary Proof of Matrix-Tree Theorem for Signed Graphs." Algebra Colloquium 30, no. 03 (August 29, 2023): 493–502. http://dx.doi.org/10.1142/s1005386723000408.

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A signed graph [Formula: see text] is a graph [Formula: see text] with vertex set [Formula: see text] and edge set [Formula: see text], together with a function [Formula: see text] assigning a positive or negative sign to each edge. In this paper, we present a more elementary proof for the matrix-tree theorem of signed graphs, which is based on the relations between the incidence matrices and the Laplcians of signed graphs. As an application, we also obtain the results of Monfared and Mallik about the matrix-tree theorem of graphs for signless Laplacians.

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Brown, John, Chris Godsil, Devlin Mallory, Abigail Raz, and Christino Tamon. "Perfect state transfer on signed graphs." Quantum Information and Computation 13, no. 5&6 (May 2013): 511–30. http://dx.doi.org/10.26421/qic13.5-6-10.

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We study perfect state transfer of quantum walks on signed graphs. Our aim is to show that negative edges are useful for perfect state transfer. First, we show that the signed join of a negative $2$-clique with any positive $(n,3)$-regular graph has perfect state transfer even if the unsigned join does not. Curiously, the perfect state transfer time improves as $n$ increases. Next, we prove that a signed complete graph has perfect state transfer if its positive subgraph is a regular graph with perfect state transfer and its negative subgraph is periodic. This shows that signing is useful for creating perfect state transfer since no complete graph (except for the $2$-clique) has perfect state transfer. Also, we show that the double-cover of a signed graph has perfect state transfer if the positive subgraph has perfect state transfer and the negative subgraph is periodic.Here, signing is useful for constructing unsigned graphs with perfect state transfer. Finally, we study perfect state transfer on a family of signed graphs called the exterior powers which is derived from a many-fermion quantum walk on graphs.

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Dissertations / Theses on the topic "THEORY OF SIGNED GRAPHS"

1

Bowlin, Garry. "Maximum frustration of bipartite signed graphs." Diss., Online access via UMI:, 2009.

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Wang, Jue. "Algebraic structures of signed graphs /." View abstract or full-text, 2007. http://library.ust.hk/cgi/db/thesis.pl?MATH%202007%20WANG.

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Sen, Sagnik. "A contribution to the theory of graph homomorphisms and colorings." Phd thesis, Bordeaux, 2014. http://tel.archives-ouvertes.fr/tel-00960893.

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Dans cette thèse, nous considérons des questions relatives aux homomorphismes de quatre types distincts de graphes : les graphes orientés, les graphes orientables, les graphes 2-arête colorés et les graphes signés. Pour chacun des ces quatre types, nous cherchons à déterminer le nombre chromatique, le nombre de clique relatif et le nombre de clique absolu pour différentes familles de graphes planaires : les graphes planaires extérieurs, les graphes planaires extérieurs de maille fixée, les graphes planaires et les graphes planaires de maille fixée. Nous étudions également les étiquetages "2-dipath" et "L(p,q)" des graphes orientés et considérons les catégories des graphes orientables et des graphes signés. Nous étudions enfin les différentes relations pouvant exister entre ces quatre types d'homomorphismes de graphes.

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Sivaraman, Vaidyanathan. "Some Topics concerning Graphs, Signed Graphs and Matroids." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1354645035.

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Sun, Qiang. "A contribution to the theory of (signed) graph homomorphism bound and Hamiltonicity." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLS109/document.

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Dans cette thèse, nous etudions deux principaux problèmes de la théorie des graphes: problème d’homomorphisme des graphes planaires (signés) et problème de cycle hamiltonien.Comme une extension du théorème des quatre couleurs, il est conjecturé([80], [41]) que chaque graphe signé cohérent planaire de déséquilibré-maille d+1(d>1) admet un homomorphisme à cube projective signé SPC(d) de dimension d. La question suivant étalés naturelle:Est-ce que SPC(d) une borne optimale de déséquilibré-maille d+1 pour tous les graphes signés cohérente planaire de déséquilibré-maille d+1?Au Chapitre 2, nous prouvons que: si (B,Ω) est un graphe signé cohérente dedéséquilibré-maille d qui borne la classe des graphes signés cohérents planaires de déséquilibré-maille d+1, puis |B| ≥2^{d−1}. Notre résultat montre que si la conjecture ci-dessus est vérifiée, alors le SPC(d) est une borne optimale à la fois en terme du nombre des sommets et du nombre de arêtes.Lorsque d=2k, le problème est équivalent aux problème des graphes:est-ce que PC(2k) une borne optimale de impair-maille 2k+1 pour P_{2k+1} (tous les graphes planaires de impair-maille au moins 2k+1)? Notez que les graphes K_4-mineur libres sont les graphes planaires, est PC(2k) aussi une borne optimale de impair-maille 2k+1 pour tous les graphes K_4-mineur libres de impair-maille 2k+1? La réponse est négative, dans[6], est donné une famille de graphes d’ordre O(k^2) que borne les graphes K_4-mineur libres de impair-maille 2k+1. Est-ce que la borne optimale? Au Chapitre 3, nous prouvons que: si B est un graphe de impair-maille 2k+1 qui borne tous les graphes K_4-mineur libres de impair-maille 2k+1, alors |B|≥(k+1)(k+2)/2. La conjonction de nos résultat et le résultat dans [6] montre que l’ordre O(k^2) est optimal. En outre, si PC(2k) borne P_{2k+1}, PC(2k) borne également P_{2r+1}(r>k).Cependant, dans ce cas, nous croyons qu’un sous-graphe propre de P(2k) serait suffisant à borner P_{2r+1}, alors quel est le sous-graphe optimal de PC2k) qui borne P_{2r+1}? Le premier cas non résolu est k=3 et r= 5. Dans ce cas, Naserasr [81] a conjecturé que le graphe Coxeter borne P_{11}. Au Chapitre 4, nous vérifions cette conjecture pour P_{17}.Au Chapitres 5, 6, nous étudions les problèmes du cycle hamiltonien. Dirac amontré en 1952 que chaque graphe d’ordre n est hamiltonien si tout sommet a un degré au moins n/2. Depuis, de nombreux résultats généralisant le théorème de Dirac sur les degré ont été obtenus. Une approche consiste à construire un cycle hamiltonien à partir d'un ensemble de sommets en contrôlant leur position sur le cycle. Dans cette thèse, nous considérons deux conjectures connexes. La première est la conjecture d'Enomoto: si G est un graphe d’ordre n≥3 et δ(G)≥n/2+1, pour toute paire de sommets x,y dans G, il y a un cycle hamiltonien C de G tel que dist_C(x,y)=n/2.Notez que l’ ́etat de degre de la conjecture de Enomoto est forte. Motivé par cette conjecture, il a prouvé, dans [32], qu’une paire de sommets peut être posé des distances pas plus de n/6 sur un cycle hamiltonien. Dans [33], les cas δ(G)≥(n+k)/2 sont considérés, il a prouvé qu’une paire de sommets à une distance entre 2 à k peut être posé sur un cycle hamiltonien. En outre, Faudree et Li ont proposé une conjecture plus générale: si G est un graphe d’ordre n≥3 et δ(G)≥n/2+1, pour toute paire de sommets x,y dans G et tout entier 2≤k≤n/2, il existe un cycle hamiltonien C de G tel que dist_C(x,y)=k. Utilisant de Regularity Lemma et Blow-up Lemma, au chapitre 5, nous donnons une preuve de la conjeture d'Enomoto conjecture pour les graphes suffisamment grand, et dans le chapitre 6, nous donnons une preuve de la conjecture de Faudree et Li pour les graphe suffisamment grand
In this thesis, we study two main problems in graph theory: homomorphism problem of planar (signed) graphs and Hamiltonian cycle problem.As an extension of the Four-Color Theorem, it is conjectured ([80],[41]) that every planar consistent signed graph of unbalanced-girth d+1(d>1) admits a homomorphism to signed projective cube SPC(d) of dimension d. It is naturally asked that:Is SPC(d) an optimal bound of unbalanced-girth d+1 for all planar consistent signed graphs of unbalanced-girth d+1?In Chapter 2, we prove that: if (B,Ω) is a consistent signed graph of unbalanced-girth d which bounds the class of consistent signed planar graphs of unbalanced-girth d, then |B|≥2^{d-1}. Furthermore,if no subgraph of (B,Ω) bounds the same class, δ(B)≥d, and therefore,|E(B)|≥d·2^{d-2}.Our result shows that if the conjecture above holds, then the SPC(d) is an optimal bound both in terms of number of vertices and number of edges.When d=2k, the problem is equivalent to the homomorphisms of graphs: isPC(2k) an optimal bound of odd-girth 2k+1 for P_{2k+1}(the class of all planar graphs of odd-girth at least 2k+1)? Note that K_4-minor free graphs are planar graphs, is PC(2k) also an optimal bound of odd-girth 2k+1 for all K_4-minor free graphs of odd-girth 2k+1 ? The answer is negative, in [6], a family of graphs of order O(k^2) bounding the K_4-minor free graphs of odd-girth 2k+1 were given. Is this an optimal bound? In Chapter 3, we prove that: if B is a graph of odd-girth 2k+1 which bounds all the K_4-minor free graphs of odd-girth 2k+1,then |B|≥(k+1)(k+2)/2. Our result together with the result in [6] shows that order O(k^2) is optimal.Furthermore, if PC(2k) bounds P_{2k+1},then PC(2k) also bounds P_{2r+1}(r>k). However, in this case we believe that a proper subgraph of PC(2k) would suffice to bound P_{2r+1}, then what’s the optimal subgraph of PC(2k) that bounds P_{2r+1}? The first case of this problem which is not studied is k=3 and r=5. For this case, Naserasr [81] conjectured that the Coxeter graph bounds P_{11} . Supporting this conjecture, in Chapter 4, we prove that the Coxeter graph bounds P_{17}.In Chapter 5,6, we study the Hamiltonian cycle problems. Dirac showed in 1952that every graph of order n is Hamiltonian if any vertex is of degree at least n/2. This result started a new approach to develop sufficient conditions on degrees for a graph to be Hamiltonian. Many results have been obtained in generalization of Dirac’s theorem. In the results to strengthen Dirac’s theorem, there is an interesting research area: to control the placement of a set of vertices on a Hamiltonian cycle such that thesevertices have some certain distances among them on the Hamiltonian cycle.In this thesis, we consider two related conjectures, one is given by Enomoto: if G is a graph of order n≥3, and δ(G)≥n/2+1, then for any pair of vertices x, y in G, there is a Hamiltonian cycle C of G such that dist_C(x, y)=n/2. Motivated by this conjecture, it is proved,in [32],that a pair of vertices are located at distances no more than n/6 on a Hamiltonian cycle. In [33], the cases δ(G) ≥(n+k)/2 are considered, it is proved that a pair of vertices can be located at any given distance from 2 to k on a Hamiltonian cycle. Moreover, Faudree and Li proposed a more general conjecture: if G is a graph of order n≥3, and δ(G)≥n/2+1, then for any pair of vertices x, y in G andany integer 2≤k≤n/2, there is a Hamiltonian cycle C of G such that dist_C(x, y) = k. Using Regularity Lemma and Blow-up Lemma, in Chapter 5, we give a proof ofEnomoto’s conjecture for graphs of sufficiently large order, and in Chapter 6, we give a proof of Faudree and Li’s conjecture for graphs of sufficiently large order

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Kotzagiannidis, Madeleine S. "From spline wavelet to sampling theory on circulant graphs and beyond : conceiving sparsity in graph signal processing." Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/56614.

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Graph Signal Processing (GSP), as the field concerned with the extension of classical signal processing concepts to the graph domain, is still at the beginning on the path toward providing a generalized theory of signal processing. As such, this thesis aspires to conceive the theory of sparse representations on graphs by traversing the cornerstones of wavelet and sampling theory on graphs. Beginning with the novel topic of graph spline wavelet theory, we introduce families of spline and e-spline wavelets, and associated filterbanks on circulant graphs, which lever- age an inherent vanishing moment property of circulant graph Laplacian matrices (and their parameterized generalizations), for the reproduction and annihilation of (exponen- tial) polynomial signals. Further, these families are shown to provide a stepping stone to generalized graph wavelet designs with adaptive (annihilation) properties. Circulant graphs, which serve as building blocks, facilitate intuitively equivalent signal processing concepts and operations, such that insights can be leveraged for and extended to more complex scenarios, including arbitrary undirected graphs, time-varying graphs, as well as associated signals with space- and time-variant properties, all the while retaining the focus on inducing sparse representations. Further, we shift from sparsity-inducing to sparsity-leveraging theory and present a novel sampling and graph coarsening framework for (wavelet-)sparse graph signals, inspired by Finite Rate of Innovation (FRI) theory and directly building upon (graph) spline wavelet theory. At its core, the introduced Graph-FRI-framework states that any K-sparse signal residing on the vertices of a circulant graph can be sampled and perfectly reconstructed from its dimensionality-reduced graph spectral representation of minimum size 2K, while the structure of an associated coarsened graph is simultaneously inferred. Extensions to arbitrary graphs can be enforced via suitable approximation schemes. Eventually, gained insights are unified in a graph-based image approximation framework which further leverages graph partitioning and re-labelling techniques for a maximally sparse graph wavelet representation.

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Lucas, Claire. "Trois essais sur les relations entre les invariants structuraux des graphes et le spectre du Laplacien sans signe." Phd thesis, Ecole Polytechnique X, 2013. http://pastel.archives-ouvertes.fr/pastel-00956183.

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Le spectre du Laplacien sans signe a fait l'objet de beaucoup d'attention dans la communauté scientifique ces dernières années. La principale raison est l'intuition, basée sur une étude des petits graphes et sur des propriétés valides pour des graphes de toutes tailles, que plus de graphes sont déterminés par le spectre de cette matrice que par celui de la matrice d'adjacence et du Laplacien. Les travaux présentés dans cette thèse ont apporté des éléments nouveaux sur les informations contenues dans le spectre cette matrice. D'une part, on y présente des relations entre les invariants de structure et une valeur propre du Laplacien sans signe. D'autre part, on présente des familles de graphes extrêmes pour deux de ses valeurs propres, avec et sans contraintes additionnelles sur la forme de graphe. Il se trouve que ceux-ci sont très similaires à ceux obtenus dans les mêmes conditions avec les valeurs propres de la matrice d'adjacence. Cela aboutit à la définition de familles de graphes pour lesquelles, le spectre du Laplacien sans signe ou une de ses valeurs propres, le nombre de sommets et un invariant de structure suffisent à déterminer le graphe. Ces résultats, par leur similitude avec ceux de la littérature viennent confirmer l'idée que le Laplacien sans signe détermine probablement aussi bien les graphes que la matrice d'adjacence.

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Mutar, Mohammed A. "Hamiltonicity in Bidirected Signed Graphs and Ramsey Signed Numbers." Wright State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=wright1513377549200572.

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Kang, Yingli [Verfasser]. "Coloring of signed graphs / Yingli Kang." Paderborn : Universitätsbibliothek, 2018. http://d-nb.info/1153824663/34.

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Omeroglu, Nurettin Burak. "K-way Partitioning Of Signed Bipartite Graphs." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614817/index.pdf.

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Clustering is the process in which data is differentiated, classified according to some criteria. As a result of partitioning process, data is grouped into clusters for specific purpose. In a social network, clustering of people is one of the most popular problems. Therefore, we mainly concentrated on finding an efficient algorithm for this problem. In our study, data is made up of two types of entities (e.g., people, groups vs. political issues, religious beliefs) and distinct from most previous works, signed weighted bipartite graphs are used to model relations among them. For the partitioning criterion, we use the strength of the opinions between the entities. Our main intention is to partition the data into k-clusters so that entities within clusters represent strong relationship. One such example from a political domain is the opinion of people on issues. Using the signed weights on the edges, these bipartite graphs can be partitioned into two or more clusters. In political domain, a cluster represents strong relationship among a group of people and a group of issues. After partitioning, each cluster in the result set contains like-minded people and advocated issues. Our work introduces a general mechanism for k-way partitioning of signed bipartite graphs. One of the great advantages of our thesis is that it does not require any preliminary information about the structure of the input dataset. The idea has been illustrated on real and randomly generated data and promising results have been shown.

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Books on the topic "THEORY OF SIGNED GRAPHS"

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Graphs. 2nd ed. Amsterdam: North Holland, 1985.

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Kandasamy, W. B. Vasantha. Groups as graphs. Slatina, Judetul Olt, Romania: Editura CuArt, 2009.

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Cvetković, Dragoš M. Eigenspaces of graphs. Cambridge: Cambridge University Press, 2008.

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Pesch, Erwin. Retracts of graphs. Frankfurt am Main: Athenaum, 1988.

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Cvetković, Dragoš M. Eigenspaces of graphs. Cambridge: Cambridge University Press, 1997.

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Borinsky, Michael. Graphs in Perturbation Theory. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-03541-9.

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Thulasiraman, K., and M. N. S. Swamy. Graphs: Theory and Algorithms. Hoboken, NJ, USA: John Wiley & Sons, Inc., 1992. http://dx.doi.org/10.1002/9781118033104.

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S, Swamy M. N., ed. Graphs: Theory and algorithms. New York: Wiley, 1992.

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Berge, Claude. The theory of graphs. Mineola, N.Y: Dover, 2001.

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H, Haemers Willem, and SpringerLink (Online service), eds. Spectra of Graphs. New York, NY: Andries E. Brouwer and Willem H. Haemers, 2012.

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Book chapters on the topic "THEORY OF SIGNED GRAPHS"

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Pranjali and Amit Kumar. "Algebraic Signed Graphs: A Review." In Recent Advancements in Graph Theory, 261–71. Boca Raton : CRC Press, 2020. | Series: Mathematical engineering, manufacturing, and management sciences: CRC Press, 2020. http://dx.doi.org/10.1201/9781003038436-22.

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Naserasr, Reza, Edita Rollovâ, and Éric Sopena. "Homomorphisms of signed bipartite graphs." In The Seventh European Conference on Combinatorics, Graph Theory and Applications, 345–50. Pisa: Scuola Normale Superiore, 2013. http://dx.doi.org/10.1007/978-88-7642-475-5_55.

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Vijayakumar, G. R., and N. M. Singhi. "Some Recent Results on Signed Graphs with Least Eigenvalues ≥ -2." In Coding Theory and Design Theory, 213–18. New York, NY: Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4613-8994-1_16.

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Naserasr, Reza, Edita Rollová, and Éric Sopena. "On homomorphisms of planar signed graphs to signed projective cubes." In The Seventh European Conference on Combinatorics, Graph Theory and Applications, 271–76. Pisa: Scuola Normale Superiore, 2013. http://dx.doi.org/10.1007/978-88-7642-475-5_44.

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Steffen, Eckhard, and Michael Schubert. "Nowhere-zero flows on signed regular graphs." In The Seventh European Conference on Combinatorics, Graph Theory and Applications, 621–22. Pisa: Scuola Normale Superiore, 2013. http://dx.doi.org/10.1007/978-88-7642-475-5_102.

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Agrawal, Kalin, and William H. Batchelder. "Cultural Consensus Theory: Aggregating Signed Graphs under a Balance Constraint." In Social Computing, Behavioral - Cultural Modeling and Prediction, 53–60. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-29047-3_7.

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Bonchi, Filippo, Paweł Sobociński, and Fabio Zanasi. "A Categorical Semantics of Signal Flow Graphs." In CONCUR 2014 – Concurrency Theory, 435–50. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-44584-6_30.

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da Silva, Ilda P. F. "Reconstruction of a Rank 3 Oriented Matroids from its Rank 2 Signed Circuits." In Graph Theory in Paris, 355–64. Basel: Birkhäuser Basel, 2006. http://dx.doi.org/10.1007/978-3-7643-7400-6_28.

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Rahaman, Inzamam, and Patrick Hosein. "Extending DeGroot Opinion Formation for Signed Graphs and Minimizing Polarization." In Complex Networks & Their Applications IX, 298–309. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-65351-4_24.

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Alam, Jahangir, Guoqing Hu, Hafiz Md Hasan Babu, and Huazhong Xu. "Automatic Control Systems, Block Diagrams, and Signal Flow Graphs." In Control Engineering Theory and Applications, 161–204. Boca Raton: CRC Press, 2022. http://dx.doi.org/10.1201/9781003293859-3.

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Conference papers on the topic "THEORY OF SIGNED GRAPHS"

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Varma, Rohan A., and Jelena Kovacevic. "SAMPLING THEORY FOR GRAPH SIGNALS ON PRODUCT GRAPHS." In 2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP). IEEE, 2018. http://dx.doi.org/10.1109/globalsip.2018.8646362.

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Narang, Sunil K., and Antonio Ortega. "Downsampling graphs using spectral theory." In ICASSP 2011 - 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2011. http://dx.doi.org/10.1109/icassp.2011.5947281.

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Pena, Rodrigo, Xavier Bresson, and Pierre Vandergheynst. "Source localization on graphs via ℓ1 recovery and spectral graph theory." In 2016 IEEE 12th Image, Video, and Multidimensional Signal Processing Workshop (IVMSP). IEEE, 2016. http://dx.doi.org/10.1109/ivmspw.2016.7528230.

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Susymary, J., and R. Lawrance. "Graph theory analysis of protein-protein interaction graphs through clustering method." In 2017 IEEE International Conference on Intelligent Techniques in Control, Optimization and Signal Processing (INCOS). IEEE, 2017. http://dx.doi.org/10.1109/itcosp.2017.8303125.

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Vaidyanathan, Palghat P., and Oguzhan Teke. "Extending classical multirate signal processing theory to graphs." In Wavelets and Sparsity XVII, edited by Yue M. Lu, Manos Papadakis, and Dimitri Van De Ville. SPIE, 2017. http://dx.doi.org/10.1117/12.2272362.

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Kotzagiannidis, Madeleine S., and Pier Luigi Dragotti. "The graph FRI framework-spline wavelet theory and sampling on circulant graphs." In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2016. http://dx.doi.org/10.1109/icassp.2016.7472904.

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Tan, Yu, Nicholas Chua, Clarence Koh, and Anand Bhojan. "RTSDF: Real-time Signed Distance Fields for Soft Shadow Approximation in Games." In 17th International Conference on Computer Graphics Theory and Applications. SCITEPRESS - Science and Technology Publications, 2022. http://dx.doi.org/10.5220/0010996200003124.

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Loeliger, Hans-Andrea, and C. Reller. "Signal processing with factor graphs: Beamforming and Hilbert transform." In 2013 Information Theory and Applications Workshop (ITA 2013). IEEE, 2013. http://dx.doi.org/10.1109/ita.2013.6502952.

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Wu, Guohua, Liguo Zhang, and Jiejuan Tong. "Online Fault Diagnosis of Nuclear Power Plants Using Signed Directed Graph and Fuzzy Theory." In 2017 25th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/icone25-66367.

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When nuclear power plant (NPPs) is in fault, it may release radioactivity into the environment. Therefore, extremely high safety standards specification are required during its working. So it is critically important for fault detection and diagnosis (FDD). NPPs are composed of large and complex systems, it is of great significance to obtain the up-to-date information of NPPs’ running state. So FDD is used to provide the state of system accurately and timely in NPPs. Signed directed graph (SDG) can show the complex relationship between parameters and has advantages of conveniently modeling, flexible inference and so on, so SDG is adopted for FDD. To achieve SDG inference better, fuzzy theory is utilized for signal processing in the paper. Firstly, SDG model is built according to the basic steps and principles of SDG modeling, and the parameters are divided into three states which is monitored by fuzzy theory. Secondly, according to the status of parameters, SDG is used for FDD and to reveal the fault propagation path, thus possibility of each fault occurred is achieved. Finally, to verify the validity of the method, the simulation experiments are done for NPPs and the simulation experiments show that SDG-fuzzy theory framework for FDD can get the fault possibility and deeply explain the reasons of fault.

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Miller, Benjamin A., Nadya T. Bliss, and Patrick J. Wolfe. "Toward signal processing theory for graphs and non-Euclidean data." In 2010 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2010. http://dx.doi.org/10.1109/icassp.2010.5494930.

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Reports on the topic "THEORY OF SIGNED GRAPHS"

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Gennip, Yves van, Nestor Guillen, Braxton Osting, and Andrea L. Bertozzi. Mean Curvature, Threshold Dynamics, and Phase Field Theory on Finite Graphs. Fort Belvoir, VA: Defense Technical Information Center, June 2013. http://dx.doi.org/10.21236/ada581612.

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Mesbahi, Mehran. Dynamic Security and Robustness of Networked Systems: Random Graphs, Algebraic Graph Theory, and Control over Networks. Fort Belvoir, VA: Defense Technical Information Center, February 2012. http://dx.doi.org/10.21236/ada567125.

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Perl, Avichai, Bruce I. Reisch, and Ofra Lotan. Transgenic Endochitinase Producing Grapevine for the Improvement of Resistance to Powdery Mildew (Uncinula necator). United States Department of Agriculture, January 1994. http://dx.doi.org/10.32747/1994.7568766.bard.

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The original objectives are listed below: 1. Design vectors for constitutive expression of endochitinase from Trichoderma harzianum strain P1. Design vectors with signal peptides to target gene expression. 2. Extend transformation/regeneration technology to other cultivars of importance in the U.S. and Israel. 3. Transform cultivars with the endochitinase constructs developed as part of objective 1. A. Characterize foliar powdery mildew resistance in transgenic plants. Background of the topic Conventional breeding of grapevines is a slow and imprecise process. The long generation cycle, large space requirements and poor understanding of grapevine genetics prevent rapid progress. There remains great need to improve existing important cultivars without the loss of identity that follows from hybridization. Powdery mildew (Uncinula necator) is the most important fungal pathogen of grapevines, causing economic losses around the world. Genetic control of powdery mildew would reduce the requirement for chemical or cultural control of the disease. Yet, since the trait is under polygenic control, it is difficult to manipulate through hybridization and breeding. Also, because grapevines are heterozygous and vegetatively propagated cultivar identity is lost in the breeding process. Therefore, there is great need for techniques to produce transgenic versions of established cultivars with heterologous genes conferring disease resistance. Such a gene is now available for control of powdery mildew of grapevines. The protein coded by the Endochitinase gene, derived from Trichoderma harzianum, is very effective in suppressing U. necator growth. The goal of this proposal is to develop transgenic grapevines with this antifungal gene, and to test the effect of this gene on resistance to powdery mildew. Conclusions, achievements and implications Gene transfer technology for grape was developed using commercial cultivars for both wine and table grapes. It paved the way for a new tool in grapevine genetic studies enabling the alteration of specific important traits while maintaining the essential features of existing elite cultivars. Regeneration and transformation technologies were developed and are currently at an advanced stage for USA wine and Israeli seedless cultivars, representing the cutting edge of grape genetic engineering studies worldwide. Transgenic plants produced are tested for powdery mildew resistance in greenhouse and field experiments at both locations. It is our ultimate goal to develop transgenic grapes which will be more efficient and economical for growers to produce, while also providing consumers with familiar products grown with reduced chemical inputs.

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Christensen, Lance. PR-459-133750-R03 Fast Accurate Automated System To Find And Quantify Natural Gas Leaks. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), November 2019. http://dx.doi.org/10.55274/r0011633.

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Miniature natural gas sensors weighing a few hundred grams with 10 ppb s-1 sensitivity towards methane and ppb s-1 sensitivity towards methane and ethane present the energy industry with cost effective ways to improve safety, comply with State and Federal regulations, decrease natural gas emissions, and attribute natural gas indications to thermogenic or biogenic sources. One particularly promising implementation is on small unmanned aerial systems (sUASs) flown by service providers or in-house personnel or even more ambitiously as part of larger network conducting autonomous, continual monitoring. This report describes refinement of the OPLS measurement system to include all ancillary instruments needed to put OPLS methane and ethane measurements into context for leak surveillance, localization, and quantification. Flights were conducted on a variety of VTOLs and fixed wing drones as described below to ensure that the overall system development resulted in a system that was platform agnostic. This report describes: - The complete agnostic OPLS measurement system.The individual components are described and their performance investigated.Technical issues that arose during testing and field deployment are described. - Field experiments of the refined OPLS measurement system at a real-world oil and gas production site.These experiments exercise the OPLS system's ability to do leak surveillance, localization, and quantification. - Laboratory development of the OPLS instrument to improve its performance in terms of signal-to-noise and accuracy. - Field experiments demonstrating the successful application of OPLS on a fixed-wing hybrid flown at altitudes higher than 50 m. - Field experiments demonstrating the utility of source attribution using the ethane measurement capability. There is a related webinar.

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Hrebeniuk, Bohdan V. Modification of the analytical gamma-algorithm for the flat layout of the graph. [б. в.], December 2018. http://dx.doi.org/10.31812/123456789/2882.

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The planarity of graphs is one of the key sections of graph theory. Although a graph is an abstract mathematical object, most often it is graph visualization that makes it easier to study or develop in a particular area, for example, the infrastructure of a city, a company’s management or a website’s web page. In general, in the form of a graph, it is possible to depict any structures that have connections between the elements. But often such structures grow to such dimensions that it is difficult to determine whether it is possible to represent them on a plane without intersecting the bonds. There are many algorithms that solve this issue. One of these is the gamma method. The article identifies its problems and suggests methods for solving them, and also examines ways to achieve them.

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Cram, Jana, Mary Levandowski, Kaci Fitzgibbon, and Andrew Ray. Water resources summary for the Snake River and Jackson Lake Reservoir in Grand Teton National Park and John D. Rockefeller, Jr. Memorial Parkway: Preliminary analysis of 2016 data. National Park Service, June 2021. http://dx.doi.org/10.36967/nrr-2285179.

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This report summarizes discharge and water quality monitoring data for the Snake River and Jackson Lake reservoir levels in Grand Teton National Park and John D. Rockefeller, Jr. Memorial Parkway for calendar year 2016. Annual and long-term discharge summaries and an evaluation of chemical conditions relative to state and federal water quality standards are presented. These results are considered provisional, and may be subject to change. River Discharge: Hydrographs for the Snake River at Flagg Ranch, WY, and Moose, WY, exhibit a general pattern of high early summer flows and lower baseflows occurring in late summer and fall. During much of 2016, flows at the Flagg Ranch monitoring location were similar to the 25th percentile of daily flows at that site. Peak flows at Flagg Ranch were similar to average peak flow from 1983 to 2015 but occurred eleven days earlier in the year compared to the long-term average. Peak flows and daily flows at the Moose monitoring station were below the long-term average. Peak flows occurred four days later than the long-term average. During summer months, the unnatural hydro-graph at the Moose monitoring location exhibited signs of flow regulation associated with the management of Jackson Lake. Water Quality Monitoring in the Snake River: Water quality in the Snake River exhibited seasonal variability over the sampling period. Specifically, total iron peaked during high flows. In contrast, chloride, sulfate, sodium, magnesium, and calcium levels were at their annual minimum during high flows. Jackson Lake Reservoir: Reservoir storage dynamics in Jackson Lake exhibit a pattern of spring filling associated with early snowmelt runoff reaching maximum storage in mid-summer (on or near July 1). During 2016, filling water levels and reservoir storage began to increase in Jackson Lake nearly two weeks earlier than the long-term average and coincident with increases in runoff-driven flows in the Snake River. Although peak storage in Jackson Lake was larger and occurred earlier than the long-term average, minimum storage levels were similar to the long-term average.

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Boyle, M., and Elizabeth Rico. Terrestrial vegetation monitoring at Cumberland Island National Seashore: 2020 data summary. National Park Service, September 2022. http://dx.doi.org/10.36967/2294287.

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The Southeast Coast Network (SECN) conducts long-term terrestrial vegetation monitoring as part of the nationwide Inventory and Monitoring Program of the National Park Service (NPS). The vegetation community vital sign is one of the primary-tier resources identified by SECN park managers, and it is currently conducted at 15 network parks (DeVivo et al. 2008). Monitoring plants and their associated communities over time allows for targeted understanding of ecosystems within the SECN geography, which provides managers information about the degree of change within their parks’ natural vegetation. 2020 marks the first year of conducting this monitoring effort at Cumberland Island National Seashore (CUIS). Fifty-six vegetation plots were established throughout the park from May through July. Data collected in each plot included species richness across multiple spatial scales, species-specific cover and constancy, species-specific woody stem seedling/sapling counts and adult tree (greater than 10 centimeters [3.9 inches {in}]) diameter at breast height (DBH), overall tree health, landform, soil, observed disturbance, and woody biomass (i.e., fuel load) estimates. This report summarizes the baseline (year 1) terrestrial vegetation data collected at Cumberland Island National Seashore in 2020. Data were stratified across three dominant broadly defined habitats within the park, including Coastal Plain Upland Open Woodlands, Maritime Open Upland Grasslands, and Maritime Upland Forests and Shrublands. Noteworthy findings include: 213 vascular plant taxa (species or lower) were observed across 56 vegetation plots, including 12 species not previously documented within the park. The most frequently encountered species in each broadly defined habitat included: Coastal Plain Upland Open Woodlands: longleaf + pond pine (Pinus palustris; P. serotina), redbay (Persea borbonia), saw palmetto (Serenoa repens), wax-myrtle (Morella cerifera), deerberry (Vaccinium stamineum), variable panicgrass (Dichanthelium commutatum), and hemlock rosette grass (Dichanthelium portoricense). Maritime Open Upland Grasslands: wax-myrtle, saw greenbrier (Smilax auriculata), sea oats (Uniola paniculata), and other forbs and graminoids. Maritime Upland Forests and Shrublands: live oak (Quercus virginiana), redbay, saw palmetto, muscadine (Muscadinia rotundifolia), and Spanish moss (Tillandsia usneoides) Two non-native species, Chinaberry (Melia azedarach) and bahiagrass (Paspalum notatum), categorized as invasive by the Georgia Exotic Pest Plant Council (GA-EPPC 2018) were encountered in four different Maritime Upland Forest and Shrubland plots during this monitoring effort. Six vascular plant species listed as rare and tracked by the Georgia Department of Natural Resources (GADNR 2022) were observed in these monitoring plots, including the state listed “Rare” Florida swampprivet (Forestiera segregata var. segregata) and sandywoods sedge (Carex dasycarpa) and the “Unusual” green fly orchid (Epidendrum conopseum). Longleaf and pond pine were the most dominant species within the tree stratum of Coastal Plain Upland Open Woodland habitat types; live oak was the most dominant species of Maritime Upland Forest and Shrubland types. Saw palmetto and rusty staggerbush (Lyonia ferruginea) dominated the sapling stratum within Maritime Upland Forest and Shrubland habitat types. Of the 20 tree-sized redbay trees measured during this monitoring effort only three were living and these were observed with severely declining vigor, indicating the prevalence and recent historical impact of laurel wilt disease (LWD) across the island’s maritime forest ecosystems. There was an unexpectedly low abundance of sweet grass (Muhlenbergia sericea) and saltmeadow cordgrass (Spartina patens) within interdune swale plots of Maritime Open Upland habitats on the island, which could be a result of grazing activity by feral horses. Live oak is the dominant tree-sized species across...

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Boyle, Maxwell, and Elizabeth Rico. Terrestrial vegetation monitoring at Fort Pulaski National Monument: 2019 data summary. National Park Service, December 2021. http://dx.doi.org/10.36967/nrds-2288716.

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The Southeast Coast Network (SECN) conducts long-term terrestrial vegetation monitoring as part of the nationwide Inventory and Monitoring Program of the National Park Service (NPS). The vegetation community vital sign is one of the primary-tier resources identified by SECN park managers, and monitoring is currently conducted at 15 network parks (DeVivo et al. 2008). Monitoring plants and their associated communities over time allows for targeted understanding of ecosystems within the SECN geography, which provides managers information about the degree of change within their parks’ natural vegetation. 2019 marks the first year of conducting this monitoring effort on four SECN parks, including Fort Pulaski National Monument (FOPU). Twelve vegetation plots were established at Fort Pulaski National Monument in August. Data collected in each plot included species richness across multiple spatial scales, species-specific cover and constancy, species-specific woody stem seedling/sapling counts and adult tree (greater than 10 centimeters [3.9 inches {in}]) diameter at breast height (DBH), overall tree health, landform, soil, observed disturbance, and woody biomass (i.e., fuel load) estimates. This report summarizes the baseline (year 1) terrestrial vegetation data collected at Fort Pulaski National Monument in 2019. Data were stratified across two dominant broadly defined habitats within the park (Maritime Tidal Wetlands and Maritime Upland Forests and Shrublands). Noteworthy findings include: Sixty-six vascular plant taxa were observed across 12 vegetation plots, including six taxa not previously known from the park. Plots were located on both Cockspur and McQueen’s Island. The most frequently encountered species in each broadly defined habitat included: Maritime Tidal Wetlands: smooth cordgrass (Spartina alterniflora), perennial saltmarsh aster(Symphyotrichum enuifolium), and groundsel tree (Baccharis halimifolia) Maritime Upland Forests and Shrublands: yaupon (Ilex vomitoria), southern/eastern red cedar (Juniperus silicicola + virginiana), and cabbage palmetto (Sabal palmetto). Four non-native species identified as invasive by the Georgia Exotic Pest Plant Council (GA-EPPC 2018) were found during this monitoring effort. These species (and their overall frequency of occurrence within all plots) included: Japanese honeysuckle (Lonicera japonica; 17%), bahiagrass (Paspalum notatum; 8%), Vasey’s grass (Paspalum urvillei; 8%), and European common reed (Phragmites australis; 8%). Two rare plants tracked by the Georgia Department of Natural Resources (GADNR 2013) were found during this monitoring effort. These include Florida wild privet (Forestiera segregata) and Bosc’s bluet (Oldenlandia boscii). Southern/eastern red cedar and cabbage palmetto were the most dominant species within the tree stratum of the maritime Upland Forest and Shrubland habitat type. Species that dominated the sapling and seedling strata of this type included yaupon, cabbage palmetto, groundsel tree, and Carolina laurel cherry (Prunus caroliniana). The health status of sugarberry (Celtis laevigata)—a typical canopy species in maritime forests of the South Atlantic Coastal Plain--observed on park plots appeared to be in decline, with most stems experiencing elevated levels of dieback and low vigor. Over the past decade, this species has been experiencing unexplained high rates of dieback and mortality throughout its range in the Southeastern United States; current research is focusing on what may be causing these alarming die-off patterns. Duff and litter made up the majority of downed woody biomass (fuel loads) across FOPU vegetation plots.

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Boyle, Maxwell, and Elizabeth Rico. Terrestrial vegetation monitoring at Cape Hatteras National Seashore: 2019 data summary. National Park Service, January 2022. http://dx.doi.org/10.36967/nrr-2290019.

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The Southeast Coast Network (SECN) conducts long-term terrestrial vegetation monitoring as part of the nationwide Inventory and Monitoring Program of the National Park Service (NPS). The vegetation community vital sign is one of the primary-tier resources identified by SECN park managers, and monitoring is currently conducted at 15 network parks (DeVivo et al. 2008). Monitoring plants and their associated communities over time allows for targeted understanding of ecosystems within the SECN geography, which provides managers information about the degree of change within their parks’ natural vegetation. The first year of conducting this monitoring effort at four SECN parks, including 52 plots on Cape Hatteras National Seashore (CAHA), was 2019. Twelve vegetation plots were established at Cape Hatteras NS in July and August. Data collected in each plot included species richness across multiple spatial scales, species-specific cover and constancy, species-specific woody stem seedling/sapling counts and adult tree (greater than 10 centimeters [3.9 inches {in}]) diameter at breast height (DBH), overall tree health, landform, soil, observed disturbance, and woody biomass (i.e., fuel load) estimates. This report summarizes the baseline (year 1) terrestrial vegetation data collected at Cape Hatteras National Seashore in 2019. Data were stratified across four dominant broadly defined habitats within the park (Maritime Tidal Wetlands, Maritime Nontidal Wetlands, Maritime Open Uplands, and Maritime Upland Forests and Shrublands) and four land parcels (Bodie Island, Buxton, Hatteras Island, and Ocracoke Island). Noteworthy findings include: A total of 265 vascular plant taxa (species or lower) were observed across 52 vegetation plots, including 13 species not previously documented within the park. The most frequently encountered species in each broadly defined habitat included: Maritime Tidal Wetlands: saltmeadow cordgrass Spartina patens), swallow-wort (Pattalias palustre), and marsh fimbry (Fimbristylis castanea) Maritime Nontidal Wetlands: common wax-myrtle (Morella cerifera), saltmeadow cordgrass, eastern poison ivy (Toxicodendron radicans var. radicans), and saw greenbriar (Smilax bona-nox) Maritime Open Uplands: sea oats (Uniola paniculata), dune camphorweed (Heterotheca subaxillaris), and seabeach evening-primrose (Oenothera humifusa) Maritime Upland Forests and Shrublands: : loblolly pine (Pinus taeda), southern/eastern red cedar (Juniperus silicicola + virginiana), common wax-myrtle, and live oak (Quercus virginiana). Five invasive species identified as either a Severe Threat (Rank 1) or Significant Threat (Rank 2) to native plants by the North Carolina Native Plant Society (Buchanan 2010) were found during this monitoring effort. These species (and their overall frequency of occurrence within all plots) included: alligatorweed (Alternanthera philoxeroides; 2%), Japanese honeysuckle (Lonicera japonica; 10%), Japanese stilt-grass (Microstegium vimineum; 2%), European common reed (Phragmites australis; 8%), and common chickweed (Stellaria media; 2%). Eighteen rare species tracked by the North Carolina Natural Heritage Program (Robinson 2018) were found during this monitoring effort, including two species—cypress panicgrass (Dichanthelium caerulescens) and Gulf Coast spikerush (Eleocharis cellulosa)—listed as State Endangered by the Plant Conservation Program of the North Carolina Department of Agriculture and Consumer Services (NCPCP 2010). Southern/eastern red cedar was a dominant species within the tree stratum of both Maritime Nontidal Wetland and Maritime Upland Forest and Shrubland habitat types. Other dominant tree species within CAHA forests included loblolly pine, live oak, and Darlington oak (Quercus hemisphaerica). One hundred percent of the live swamp bay (Persea palustris) trees measured in these plots were experiencing declining vigor and observed with symptoms like those caused by laurel wilt......less

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Kapulnik, Yoram, Maria J. Harrison, Hinanit Koltai, and Joseph Hershenhorn. Targeting of Strigolacatones Associated Pathways for Conferring Orobanche Resistant Traits in Tomato and Medicago. United States Department of Agriculture, July 2011. http://dx.doi.org/10.32747/2011.7593399.bard.

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This proposal is focused on examination of two plant interactions: parasitic with Orobanche, and symbiosis with arbuscular mycorrhiza fungi (AMF), and the involvement of a newly define plant hormones, strigolactones (SLs), in these plant interactions. In addition to strigolactones role in regulation of above-ground plant architecture, they are also known to be secreted from roots, and to be a signal for seed germination of the parasitic plants Orobanche. Moreover, secreted strigolactones were recognized as inducers of AMFhyphae branching. The present work was aimed at Generation of RNAi mutants of both tomato and Medicago, targeting multiple genes that may be involved in strigolactone production, carotenoid biosynthesis pathway, Pi signaling or other metabolic pathways, and hence affect AMF colonization and/or Orobanche resistance. Following the newly formed and existing RNAi mutants were examined for AMF colonization and Orobanche resistance. At the first phase of this project Orobanche seed germination assays and AMF colonization were examined in intact plants. These assays were shown to be effective and resulted with enhancement of Orobanche seed germination and AMF colonization in WT tomato plants, whereas roots of strigolactones impaired lines did not result with Orobanche seed germination and mycorrhiza colonization. Unexpectedly, root organ cultures (ROC) that were produced from the same wild type (WT) and mutant lines did not induce the Orobanche seed germination and AMFhyphal branching. This implies that under in vitro conditions ROC cultures are missing an important component for induction of Orobanche seed germination and AMFhyphal branching. In another line of experiments we have tested transgenic lines of Medicagotruncatula for AMFhuyphal branching and Orobanche seed germination assays. These lines included lines silenced for a GRAS transcription factor (RNAi 1845), an NBS-LRR type resistance gene (RNAi 1847), a kinase (RNAi 2403) and a protein of unknown function (RNAi 2417). In all cases, five independent transgenic root lines showed altered AMFphenotypes with reduced or aberrant colonization patterns. Following, we transformed tomato plants with the M. truncatulaTC 127050 PhosphoinositidekinaseRNAi construct. Transgenic lines that contained GUS constructs were used as control. All transgenic lines showed reduced level of Orobanche seed germination, masking any strigoalctones-specific effect. The research demonstrated that SLs production may not be examined in ROC –based bioassays. It was shown by the 3 independent assays employed in this project that none of the recognized characters of SLs may be reflected in these bioassays. However, when the whole plant root exudates were examined, SLs activity in root exudates was demonstrated. Hence, it can be concluded that the presence of an intact shoot, and possibly, shoot factors, may be necessary for production of SLs in roots. Another point of interest that rises from these results is that the presence of SLs is not necessary for AMF completion of life cycle. Hence, it may be concluded that SLs are important for AMFhyphal branching, before symbiosis, but not essential for AMF colonization and life cycle completion under ROC system conditions.

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