Relevant bibliographies by topics / Graphs

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Graphs'

Author: Grafiati
Published: 4 June 2021
Last updated: 19 October 2024

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Journal articles on the topic "Graphs"

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Hamidi, M. "Zero Divisor Graphs Based on General Hyperrings‎." Journal of Algebraic Hyperstructures and Logical Algebras 4, no. 2 (2023): 131–49. http://dx.doi.org/10.61838/kman.jahla.4.2.9.

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This paper introduces the concepts of reproduced general hyperring and valued-orderable general hyperring and investigates some properties of these classes of general hyperrings‎. ‎It presents the notions of‎ ‎zero divisors and zero divisor graphs are founded on the absorbing elements of general hyperrings‎. ‎General hyperrings can have more than one zeroing element‎, ‎and therefore‎, ‎based on the zeroing elements‎, ‎multiple zero divisors can be obtained‎. ‎In this study‎, ‎we discuss the isomorphism of zero divisor graphs based on the diversity of divisors of zero divisors‎. ‎The non-empty intersection of the set of absorbing elements and the hyperproduct of zero divisors of general hyperrings play a major role in the production of zero divisor graphs‎. ‎Indeed it investigated a type classification of zero divisor graphs based on the finite general hyperrings‎. ‎We discuss the finite reproduced general hyperrings‎, ‎investigate their zero divisor graphs‎, ‎and show that an infinite reproduced general hyperring can have a finite zero divisor graph‎.
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FÜRER, MARTIN, and SHIVA PRASAD KASIVISWANATHAN. "Approximately Counting Embeddings into Random Graphs." Combinatorics, Probability and Computing 23, no. 6 (July 9, 2014): 1028–56. http://dx.doi.org/10.1017/s0963548314000339.

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LetHbe a graph, and letCH(G) be the number of (subgraph isomorphic) copies ofHcontained in a graphG. We investigate the fundamental problem of estimatingCH(G). Previous results cover only a few specific instances of this general problem, for example the case whenHhas degree at most one (the monomer-dimer problem). In this paper we present the first general subcase of the subgraph isomorphism counting problem, which is almost always efficiently approximable. The results rely on a new graph decomposition technique. Informally, the decomposition is a labelling of the vertices such that every edge is between vertices with different labels, and for every vertex all neighbours with a higher label have identical labels. The labelling implicitly generates a sequence of bipartite graphs, which permits us to break the problem of counting embeddings of large subgraphs into that of counting embeddings of small subgraphs. Using this method, we present a simple randomized algorithm for the counting problem. For all decomposable graphsHand all graphsG, the algorithm is an unbiased estimator. Furthermore, for all graphsHhaving a decomposition where each of the bipartite graphs generated is small and almost all graphsG, the algorithm is a fully polynomial randomized approximation scheme.We show that the graph classes ofHfor which we obtain a fully polynomial randomized approximation scheme for almost allGincludes graphs of degree at most two, bounded-degree forests, bounded-width grid graphs, subdivision of bounded-degree graphs, and major subclasses of outerplanar graphs, series-parallel graphs and planar graphs of large girth, whereas unbounded-width grid graphs are excluded. Moreover, our general technique can easily be applied to proving many more similar results.
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Shukur, Ali A., Akbar Jahanbani, and Haider Shelash. "The Behavior of Weighted Graph’s Orbit and Its Energy." Mathematical Problems in Engineering 2021 (May 17, 2021): 1–6. http://dx.doi.org/10.1155/2021/9933072.

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Studying the orbit of an element in a discrete dynamical system is one of the most important areas in pure and applied mathematics. It is well known that each graph contains a finite (or infinite) number of elements. In this work, we introduce a new analytical phenomenon to the weighted graphs by studying the orbit of their elements. Studying the weighted graph's orbit allows us to have a better understanding to the behaviour of the systems (graphs) during determined time and environment. Moreover, the energy of the graph’s orbit is given.
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Lakshmanan S., Aparna, S. B. Rao, and A. Vijayakumar. "Gallai and anti-Gallai graphs of a graph." Mathematica Bohemica 132, no. 1 (2007): 43–54. http://dx.doi.org/10.21136/mb.2007.133996.

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Kaviya, S., G. Mahadevan, and C. Sivagnanam. "Generalizing TCCD-Number For Power Graph Of Some Graphs." Indian Journal Of Science And Technology 17, SPI1 (April 25, 2024): 115–23. http://dx.doi.org/10.17485/ijst/v17sp1.243.

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Objective: Finding the triple connected certified domination number for the power graph of some peculiar graphs. Methods: A dominating set with the condition that every vertex in has either zero or at least two neighbors in and is triple connected is a called triple connected certified domination number of a graph. The minimum cardinality among all the triple connected certified dominating sets is called the triple connected certified domination number and is denoted by . The upper bound and lower bound of for the given graphs is found and then proved the upper bound and lower bound of were equal. Findings: We found the (TCCD)-number for the power graph of some peculiar graphs. Also, we have generalized the result for path, cycle, ladder graph, comb graph, coconut tree graph, triangular snake, alternate triangular snake, quadrilateral snake and tadpole graph. Novelty: The triple connected certified domination is a new parameter in which the certified domination holds the triple connected in induced . Keywords: Domination Number, Power Graphs, Triple Connected, Certified Domination, Triple Connected Certified Domination
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Srinivasan, Sakunthala, and Vimala Shanmugavel. "Comparative Study on Different Types of Energies." Indian Journal Of Science And Technology 17, no. 28 (July 31, 2024): 2954–59. http://dx.doi.org/10.17485/ijst/v17i28.1447.

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Objectives : The absolute sum of the eigenvalues is the definition of the graph's energy. In addition to discussing their relationship, this study compares the energy of the Adjacency matrix, Laplacian matrix, Signless Laplacian matrix, and Seidel matrix applied to ten distinct kinds of graphs. In this study, a correlation is established between the energy of graphs and the energy of Edge Antimagic graphs. Methods: The technical description of the graph's energy, . An Edge Antimagic graph's energy, identified by (G) = , is the absolute total of its eigenvalues. Findings: The energy was calculated along with its link to the energy of Edge Antimagic matrix, Adjacency matrix, Laplacian matrix, Signless Laplacian matrix, and Seidel matrix. Novelty: Edge antimagic graphs have been applied using the concept of energy. The energy of Edge Antimagic graphs and the energy of graphs were discovered to be related. An analysis was conducted comparing Adjacency energy, Seidel energy, Laplacian energy, and Signless Laplacian energy. Keywords: Laplacian Energy, Spectrum, Seidel Matrix, Signless Laplacian Matrix, Edge Antimagic Graphs.
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M, Simaringa, and Santhoshkumar K. "Prime Graphs of Some Graphs." Journal of Advanced Research in Dynamical and Control Systems 12, no. 8 (August 19, 2020): 51–55. http://dx.doi.org/10.5373/jardcs/v12i8/20202445.

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Zhang, Xiaoling, and Chengyuan Song. "The Distance Matrices of Some Graphs Related to Wheel Graphs." Journal of Applied Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/707954.

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LetDdenote the distance matrix of a connected graphG. The inertia ofDis the triple of integers (n+(D), n0(D), n-(D)), wheren+(D),n0(D), andn-(D)denote the number of positive, 0, and negative eigenvalues ofD, respectively. In this paper, we mainly study the inertia of distance matrices of some graphs related to wheel graphs and give a construction for graphs whose distance matrices have exactly one positive eigenvalue.
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Rashed, Payman A. "The Nullity of Identifying Path Graph with Some Special Graphs." Journal of Zankoy Sulaimani - Part A 19, no. 2 (November 20, 2016): 185–94. http://dx.doi.org/10.17656/jzs.10622.

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Zelinka, Bohdan. "Small directed graphs as neighbourhood graphs." Czechoslovak Mathematical Journal 38, no. 2 (1988): 269–73. http://dx.doi.org/10.21136/cmj.1988.102221.

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Dissertations / Theses on the topic "Graphs"

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Hearon, Sean M. "PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS." CSUSB ScholarWorks, 2016. https://scholarworks.lib.csusb.edu/etd/427.

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A graph is planar if it can be drawn on a piece of paper such that no two edges cross. The smallest complete and complete bipartite graphs that are not planar are K5 and K{3,3}. A biplanar graph is a graph whose edges can be colored using red and blue such that the red edges induce a planar subgraph and the blue edges induce a planar subgraph. In this thesis, we determine the smallest complete and complete bipartite graphs that are not biplanar.
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Duffy, Christopher. "Homomorphisms of (j, k)-mixed graphs." Thesis, Bordeaux, 2015. http://hdl.handle.net/1828/6601.

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A mixed graph is a simple graph in which a subset of the edges have been assigned directions to form arcs. For non-negative integers j and k, a (j, k)−mixed graph is a mixed graph with j types of arcs and k types of edges. The collection of (j, k)−mixed graphs contains simple graphs ((0,1)−mixed graphs), oriented graphs ((1,0)-mixed graphs) and k−edge-coloured graphs ((0, k)−mixed graphs). A homomorphism is a vertex mapping from one (j,k)−mixed graph to another in which edge type is preserved, and arc type and direction are preserved. An m−colouring of a (j, k)−mixed graph is a homomorphism from that graph to a target with m vertices. The (j, k)−chromatic number of a (j, k)−mixed graph is the least m such that an m−colouring exists. When (j, k) = (0, 1), we see that these definitions are consistent with the usual definitions of graph homomorphism and graph colouring. Similarly, when (j, k) = (1, 0) and (j, k) = (0, k) these definitions are consistent with the usual definitions of homomorphism and colouring for oriented graphs and k−edge-coloured graphs, respectively. In this thesis we study the (j, k)−chromatic number and related parameters for different families of graphs, focussing particularly on the (1, 0)−chromatic number, more commonly called the oriented chromatic number, and the (0, k)−chromatic number. In examining oriented graphs, we provide improvements to the upper and lower bounds for the oriented chromatic number of the families of oriented graphs with maximum degree 3 and 4. We generalise the work of Sherk and MacGillivray on the 2−dipath chromatic number, to consider colourings in which vertices at the ends of iii a directed path of length at most k must receive different colours. We examine the implications of the work of Smolikova on simple colourings to study of the oriented chromatic number of the family of oriented planar graphs. In examining k−edge-coloured graphs we provide improvements to the upper and lower bounds for the family of 2−edge-coloured graphs with maximum degree 3. In doing so, we define the alternating 2−path chromatic number of k−edge-coloured graphs, a parameter similar in spirit to the 2−dipath chromatic number for oriented graphs. We also consider a notion of simple colouring for k−edge-coloured graphs, and show that the methods employed by Smolikova ́ for simple colourings of oriented graphs may be adapted to k−edge-coloured graphs. In addition to considering vertex colourings, we also consider incidence colourings of both graphs and digraphs. Using systems of distinct representatives, we provide a new characterisation of the incidence chromatic number. We define the oriented incidence chromatic number and find, by way of digraph homomorphism, a connection between the oriented incidence chromatic number and the chromatic number of the underlying graph. This connection motivates our study of the oriented incidence chromatic number of symmetric complete digraphs.
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Yang, Weihua. "Supereulerian graphs, Hamiltonicity of graphes and several extremal problems in graphs." Phd thesis, Université Paris Sud - Paris XI, 2013. http://tel.archives-ouvertes.fr/tel-00877793.

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In this thesis, we focus on the following topics: supereulerian graphs, hamiltonian line graphs, fault-tolerant Hamiltonian laceability of Cayley graphs generated by transposition trees, and several extremal problems on the (minimum and/or maximum) size of graphs under a given graph property. The thesis includes six chapters. The first one is to introduce definitions and summary the main results of the thesis, and in the last chapter we introduce the furture research of the thesis. The main studies in Chapters 2 - 5 are as follows. In Chapter 2, we explore conditions for a graph to be supereulerian.In Section 1 of Chapter 2, we characterize the graphs with minimum degree at least 2 and matching number at most 3. By using the characterization, we strengthen the result in [93] and we also address a conjecture in the paper.In Section 2 of Chapter 2, we prove that if $d(x)+d(y)\geq n-1-p(n)$ for any edge $xy\in E(G)$, then $G$ is collapsible except for several special graphs, where $p(n)=0$ for $n$ even and $p(n)=1$ for $n$ odd. As a corollary, a characterization for graphs satisfying $d(x)+d(y)\geq n-1-p(n)$ for any edge $xy\in E(G)$ to be supereulerian is obtained. This result extends the result in [21].In Section 3 of Chapter 2, we focus on a conjecture posed by Chen and Lai [Conjecture~8.6 of [33]] that every 3-edge connected and essentially 6-edge connected graph is collapsible. We find a kind of sufficient conditions for a 3-edge connected graph to be collapsible.In Chapter 3, we mainly consider the hamiltonicity of 3-connected line graphs.In the first section of Chapter 3, we give several conditions for a line graph to be hamiltonian, especially we show that every 3-connected, essentially 11-connected line graph is hamilton- connected which strengthens the result in [91].In the second section of Chapter 3, we show that every 3-connected, essentially 10-connected line graph is hamiltonian-connected.In the third section of Chapter 3, we show that 3-connected, essentially 4-connected line graph of a graph with at most 9 vertices of degree 3 is hamiltonian. Moreover, if $G$ has 10 vertices of degree 3 and its line graph is not hamiltonian, then $G$ can be contractible to the Petersen graph.In Chapter 4, we consider edge fault-tolerant hamiltonicity of Cayley graphs generated by transposition trees. We first show that for any $F\subseteq E(Cay(B:S_{n}))$, if $|F|\leq n-3$ and $n\geq4$, then there exists a hamiltonian path in $Cay(B:S_{n})-F$ between every pair of vertices which are in different partite sets. Furthermore, we strengthen the above result in the second section by showing that $Cay(S_n,B)-F$ is bipancyclic if $Cay(S_n,B)$ is not a star graph, $n\geq4$ and $|F|\leq n-3$.In Chapter 5, we consider several extremal problems on the size of graphs.In Section 1 of Chapter 5, we bounds the size of the subgraph induced by $m$ vertices of hypercubes. We show that a subgraph induced by $m$ (denote $m$ by $\sum\limits_{i=0}^ {s}2^{t_i}$, $t_0=[\log_2m]$ and $t_i= [\log_2({m-\sum\limits_{r=0}^{i-1}2 ^{t_r}})]$ for $i\geq1$) vertices of an $n$-cube (hypercube) has at most $\sum\limits_{i=0}^{s}t_i2^{t_i-1} +\sum\limits_{i=0}^{s} i\cdot2^{t_i}$ edges. As its applications, we determine the $m$-extra edge-connectivity of hypercubes for $m\leq2^{[\frac{n}2]}$ and $g$-extra edge-connectivity of the folded hypercube for $g\leq n$.In Section 2 of Chapter 5, we partially study the minimum size of graphs with a given minimum degree and a given edge degree. As an application, we characterize some kinds of minimumrestricted edge connected graphs.In Section 3 of Chapter 5, we consider the minimum size of graphs satisfying Ore-condition.
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Badaoui, Mohamad. "G-graphs and Expander graphs." Thesis, Normandie, 2018. http://www.theses.fr/2018NORMC207/document.

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L’utilisation de l’algèbre pour résoudre des problèmes de graphes a conduit au développement de trois branches : théorie spectrale des graphes, géométrie et combinatoire des groupes et études des invariants de graphes. La notion de graphe d’expansions (invariant de graphes) est relativement récente, elle a été développée afin d’étudier la robustesse des réseaux de télécommunication. Il s’avère que la construction de familles infinies de graphes expanseurs est un problème difficile. Cette thèse traite principalement de la construction de nouvelles familles de tels graphes. Les graphes expanseurs possèdent des nombreuses applications en informatique, notamment dans la construction de certains algorithmes, en théorie de la complexité, sur les marches aléatoires (random walk), etc. En informatique théorique, ils sont utilisés pour construire des familles de codes correcteurs d’erreur. Comme nous l’avons déjà vu les familles d’expanseurs sont difficiles à construire. La plupart des constructions s'appuient sur des techniques algébriques complexes, principalement en utilisant des graphes de Cayley et des produit Zig-Zag. Dans cette thèse, nous présentons une nouvelle méthode de construction de familles infinies d’expanseurs en utilisant les G-graphes. Ceux-ci sont en quelque sorte une généralisation des graphes de Cayley. Plusieurs nouvelles familles infinies d’expanseurs sont construites, notamment la première famille d’expanseurs irréguliers
Applying algebraic and combinatorics techniques to solve graph problems leads to the birthof algebraic and combinatorial graph theory. This thesis deals mainly with a crossroads questbetween the two theories, that is, the problem of constructing infinite families of expandergraphs.From a combinatorial point of view, expander graphs are sparse graphs that have strongconnectivity properties. Expanders constructions have found extensive applications in bothpure and applied mathematics. Although expanders exist in great abundance, yet their explicitconstructions, which are very desirable for applications, are in general a hard task. Mostconstructions use deep algebraic and combinatorial approaches. Following the huge amountof research published in this direction, mainly through Cayley graphs and the Zig-Zagproduct, we choose to investigate this problem from a new perspective; namely by usingG-graphs theory and spectral hypergraph theory as well as some other techniques. G-graphsare like Cayley graphs defined from groups, but they correspond to an alternative construction.The reason that stands behind our choice is first a notable identifiable link between thesetwo classes of graphs that we prove. This relation is employed significantly to get many newresults. Another reason is the general form of G-graphs, that gives us the intuition that theymust have in many cases such as the relatively high connectivity property.The adopted methodology in this thesis leads to the identification of various approaches forconstructing an infinite family of expander graphs. The effectiveness of our techniques isillustrated by presenting new infinite expander families of Cayley and G-graphs on certaingroups. Also, since expanders stand in no single stem of graph theory, this brings us toinvestigate several closely related threads from a new angle. For instance, we obtain newresults concerning the computation of spectra of certain Cayley and G-graphs, and theconstruction of several new infinite classes of integral and Hamiltonian Cayley graphs
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Ramos, Garrido Lander. "Graph enumeration and random graphs." Doctoral thesis, Universitat Politècnica de Catalunya, 2017. http://hdl.handle.net/10803/405943.

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In this thesis we use analytic combinatorics to deal with two related problems: graph enumeration and random graphs from constrained classes of graphs. We are interested in drawing a general picture of some graph families by determining, first, how many elements are there of a given possible size (graph enumeration), and secondly, what is the typical behaviour of an element of fixed size chosen uniformly at random, when the size tends to infinity (random graphs). The problems concern graphs subject to global conditions, such as being planar and/or with restrictions on the degrees of the vertices. In Chapter 2 we analyse random planar graphs with minimum degree two and three. Using techniques from analytic combinatorics and the concepts of core and kernel of a graph, we obtain precise asymptotic estimates and analyse relevant parameters for random graphs, such as the number of edges or the size of the core, where we obtain Gaussian limit laws. More challenging is the extremal parameter equal to the size of the largest tree attached to the core. In this case we obtain a logarithmic estimate for the expected value together with a concentration result. In Chapter 3 we study the number of subgraphs isomorphic to a fixed graph in subcritical classes of graphs. We obtain Gaussian limit laws with linear expectation and variance when the fixed graph is 2-connected. The main tool is the analysis of infinite systems of equations by Drmota, Gittenberger and Morgenbesser, using the theory of compact operators. Computing the exact constants for the first estimates of the moments is in general out of reach. For the class of series-parallel graphs we are able to compute them in some particular interesting cases. In Chapter 4 we enumerate (arbitrary) graphs where the degree of every vertex belongs to a fixed subset of the natural numbers. In this case the associated generating functions are divergent and our analysis uses instead the so-called configuration model. We obtain precise asymptotic estimates for the number of graphs with given number of vertices and edges and subject to the degree restriction. Our results generalize widely previous special cases, such as d-regular graphs or graphs with minimum degree at least d.
En aquesta tesi utilitzem l'analítica combinatòria per treballar amb dos problemes relacionats: enumeració de grafs i grafs aleatoris de classes de grafs amb restriccions. En particular ens interessa esbossar un dibuix general de determinades famílies de grafs determinant, en primer lloc, quants grafs hi ha de cada mida possible (enumeració de grafs), i, en segon lloc, quin és el comportament típic d'un element de mida fixa triat a l'atzar uniformement, quan aquesta mida tendeix a infinit (grafs aleatoris). Els problemes en què treballem tracten amb grafs que satisfan condicions globals, com ara ésser planars, o bé tenir restriccions en el grau dels vèrtexs. En el Capítol 2 analitzem grafs planar aleatoris amb grau mínim dos i tres. Mitjançant tècniques de combinatòria analítica i els conceptes de nucli i kernel d'un graf, obtenim estimacions asimptòtiques precises i analitzem paràmetres rellevants de grafs aleatoris, com ara el nombre d'arestes o la mida del nucli, on obtenim lleis límit gaussianes. També treballem amb un paràmetre que suposa un repte més important: el paràmetre extremal que es correspon amb la mida de l'arbre més gran que penja del nucli. En aquest cas obtenim una estimació logarítmica per al seu valor esperat, juntament amb un resultat sobre la seva concentració. En el Capítol 3 estudiem el nombre de subgrafs isomorfs a un graf fix en classes de grafs subcrítiques. Quan el graf fix és biconnex, obtenim lleis límit gaussianes amb esperança i variància lineals. L'eina principal és l'anàlisi de sistemes infinits d'equacions donada per Drmota, Gittenberger i Morgenbesser, que utilitza la teoria d'operadors compactes. El càlcul de les constants exactes de la primera estimació dels moments en general es troba fora del nostre abast. Per a la classe de grafs sèrie-paral·lels podem calcular les constants en alguns casos particulars interessants. En el Capítol 4 enumerem grafs (arbitraris) el grau de cada vèrtex dels quals pertany a un subconjunt fix dels nombres naturals. En aquest cas les funcions generatrius associades són divergents i la nostra anàlisi utilitza l'anomenat model de configuració. El nostre resultat consisteix a obtenir estimacions asimptòtiques precises per al nombre de grafs amb un nombre de vèrtexs i arestes donat, amb la restricció dels graus. Aquest resultat generalitza àmpliament casos particulars existents, com ara grafs d-regulars, o grafs amb grau mínim com a mínim d.
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Khouzam, Nelly. "A new class of brittle graphs /." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66048.

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Medrano, Archie T. "Super-Euclidean graphs and super-Heisenberg graphs : their spectral and graph-theoretic properties /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1998. http://wwwlib.umi.com/cr/ucsd/fullcit?p9901440.

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Zuffi, Lorenzo. "Simplicial Complexes From Graphs Toward Graph Persistence." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13519/.

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Persistent homology is a branch of computational topology which uses geometry and topology for shape description and analysis. This dissertation is an introductory study to link persistent homology and graph theory, the connection being represented by various methods to build simplicial complexes from a graph. The methods we consider are the complex of cliques, of independent sets, of neighbours, of enclaveless sets and complexes from acyclic subgraphs, each revealing several properties of the underlying graph. Moreover, we apply the core ideas of persistence theory in the new context of graph theory, we define the persistent block number and the persistent edge-block number.
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Dusart, Jérémie. "Graph searches with applications to cocomparability graphs." Paris 7, 2014. http://www.theses.fr/2014PA077048.

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Un parcours de graphe est un mécanisme pour visiter de manière itérative les sommets d'un graphe. Cela a été une technique fondamentale dans la conception des algorithmes de graphe depuis les débuts de l'informatique. Bon nombre des premiers parcours étaient basées sur le parcours en largeur(BFS) ou en profondeur (DFS) et cela a donné des algorithmes efficaces pour les problèmes pratiques tels que la distance entre deux sommets, le diamètre, la connectivité, les problèmes de flot et la reconnaissance des graphes planaires. Le but de cette thèse est d'étudier les parcours de graphe Dans cette thèse, nous présentons des résultats généraux sur les parcours de graphe dans les graphes de cocomparabilité, mais aussi une nouvelle caractérisation des graphes de cocomparabilité et des applications des parcours de graphe pour résoudre le problème d'orientation transitive, de sous-graphe triangulé maximal, de clique séparatrice et de sommets simpliciaux. Un modèle simple et général est aussi présenté pour capturer la plupart des parcours de graphe
A graph search is a mechanism for systematically visiting the vertices of a graph. It has been a fundamental technique in the design of graph algorithms since the eraarly days of computer science. Many of the early search methods were based on Breadth First Search (BFS) or Depth First Search (DFS) and resulted in efficient algorithms for practical problems such as the distance between two vertices, diameter, connectivity, network flows and the recognition of planar graphs. The purpose of this thesis is to studied the graph search. In this thesis, we present general result about graph search in cocomparability grapj, but also a new charactrization of cocomparability graph and apllications of graph search to solve the problem of transitive orientation, maximal chordal subgraph, clique perator and simplicial vertices. A simple and general framework is also presented to capture most of the well known graph search
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Hoang, Chinh T. "Perfect graphs." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74011.

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Books on the topic "Graphs"

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Kyōto Daigaku. Sūri Kaiseki Kenkyūjo., ed. Graph equation for line graphs and m-step graphs. Kyoto, Japan: Research Institute for Mathematical Sciences, Kyoto University, 2007.

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Mikov, Aleksandr. Generalized graphs and grammars. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1013698.

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The textbook deals with ordinary graphs and their generalizations-hypergraphs, hierarchical structures, geometric graphs, random and dynamic graphs. Graph grammars are considered in detail. Meets the requirements of the federal state educational standards of higher education of the latest generation. For master's students studying in the areas of the 02.00.00 group "Computer and Information Sciences", and can also be used in senior bachelor's courses and other areas in the field of computer science and computer engineering.
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Bader, Bonnie. Graphs. New York: Grosset & Dunlap, 2003.

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Harling, Paul. Graphs. London: Ward Lock Educational, 1989.

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Alaina, Maria. Graphs. Mankato, Minn: Capstone Press, 2012.

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Harling, Paul. Graphs. London: Ward Lock Educational, 1988.

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Harling, Paul. Graphs. London: Ward Lock Educational, 1989.

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Smoothey, Marion. Graphs. New York: Marshall Cavendish, 1995.

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Harling, Paul. Graphs. London: Ward Lock Educational, 1989.

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Harling, Paul. Graphs. London: Ward Lock Educational, 1988.

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Book chapters on the topic "Graphs"

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Kimoto, Kazufumi. "Generalized Group–Subgroup Pair Graphs." In International Symposium on Mathematics, Quantum Theory, and Cryptography, 169–85. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5191-8_14.

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Abstract A regular finite graph is called a Ramanujan graph if its zeta function satisfies an analog of the Riemann Hypothesis. Such a graph has a small second eigenvalue so that it is used to construct cryptographic hash functions. Typically, explicit family of Ramanujan graphs are constructed by using Cayley graphs. In the paper, we introduce a generalization of Cayley graphs called generalized group–subgroup pair graphs, which are a generalization of group–subgroup pair graphs defined by Reyes-Bustos. We study basic properties, especially spectra of them.
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Beneš, Nikola, Luboš Brim, Samuel Pastva, and David Šafránek. "Symbolic Coloured SCC Decomposition." In Tools and Algorithms for the Construction and Analysis of Systems, 64–83. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72013-1_4.

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AbstractProblems arising in many scientific disciplines are often modelled using edge-coloured directed graphs. These can be enormous in the number of both vertices and colours. Given such a graph, the original problem frequently translates to the detection of the graph’s strongly connected components, which is challenging at this scale.We propose a new, symbolic algorithm that computes all the monochromatic strongly connected components of an edge-coloured graph. In the worst case, the algorithm performs $$O(p\cdot n\cdot \log n)$$ O ( p · n · log n ) symbolic steps, where p is the number of colours and n the number of vertices. We evaluate the algorithm using an experimental implementation based on Binary Decision Diagrams (BDDs) and large (up to $$2^{48}$$ 2 48 ) coloured graphs produced by models appearing in systems biology.
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Kurasov, Pavel. "Standard Laplacians and Secular Polynomials." In Operator Theory: Advances and Applications, 123–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 2023. http://dx.doi.org/10.1007/978-3-662-67872-5_6.

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AbstractIn this chapter we start systematic studies of spectral properties of graph Laplacians—standard Laplace operators on metric graphs. Our main interest will be families of metric graphs having the same topological structure. Metric graphs from such a family correspond to the same discrete graph but the lengths of the edges may be different. Common spectral properties of such families (and hence of all metric graphs) are best described by certain multivariate low degree polynomials.
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Paul, Sudipta, Julián Salas, and Vicenç Torra. "Edge Local Differential Privacy for Dynamic Graphs." In Security and Privacy in Social Networks and Big Data, 224–38. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-5177-2_13.

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AbstractHuge amounts of data are generated and shared in social networks and other network topologies. This raises privacy concerns when such data is not protected from leaking sensitive or personal information. Network topologies are commonly modeled through static graphs. Nevertheless, dynamic graphs better capture the temporal evolution and properties of such networks. Several differentially private mechanisms have been proposed for static graph data mining, but at the moment there are no such algorithms for dynamic data protection and mining. So, we propose two locally $$\epsilon $$ ϵ -differentially private methods for dynamic graph protection based on edge addition and deletion through the application of the noise-graph mechanism. We apply these methods to real-life datasets and show promising results preserving graph statistics for applications in community detection in time-varying networks.The main contributions of this work are: extending the definition of local differential privacy for edges to the dynamic graph domain, and showing that the community structure of the protected graphs is well preserved for suitable privacy parameters.
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Scott, Jennifer, and Miroslav Tůma. "Sparse Matrices and Their Graphs." In Nečas Center Series, 19–30. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-25820-6_2.

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AbstractMany sparse matrix algorithms exploit the close relationship between matrices and graphs. We make no assumption regarding the reader’s prior knowledge of graph theory. The purpose of this chapter is to summarize basic concepts from graph theory that will be exploited later and to establish the notation and terminology that will be used throughout.
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Anderson, David F., T. Asir, Ayman Badawi, and T. Tamizh Chelvam. "Graphs from Total Graphs." In Graphs from Rings, 351–99. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-88410-9_8.

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Mathew, Sunil, John N. Mordeson, and M. Binu. "Graphs and Weighted Graphs." In Weighted and Fuzzy Graph Theory, 1–51. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-39756-1_1.

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Ivanov, O. A. "Graphs." In Easy as π?, 85–102. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-0553-1_6.

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Aldous, Joan M., and Robin J. Wilson. "Graphs." In Graphs and Applications, 25–60. London: Springer London, 2000. http://dx.doi.org/10.1007/978-1-4471-0467-4_2.

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Allison, Lloyd. "Graphs." In Coding Ockham's Razor, 113–30. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-76433-7_11.

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Conference papers on the topic "Graphs"

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Klisura, Ðorže. "Embedding Non-planar Graphs: Storage and Representation." In 7th Student Computer Science Research Conference. University of Maribor Press, 2021. http://dx.doi.org/10.18690/978-961-286-516-0.13.

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In this paper, we propose a convention for repre-senting non-planar graphs and their least-crossing embeddings in a canonical way. We achieve this by using state-of-the-art tools such as canonical labelling of graphs, Nauty’s Graph6 string and combinatorial representations for planar graphs. To the best of our knowledge, this has not been done before. Besides, we implement the men-tioned procedure in a SageMath language and compute embeddings for certain classes of cubic, vertex-transitive and general graphs. Our main contribution is an extension of one of the graph data sets hosted on MathDataHub, and towards extending the SageMath codebase.
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Vargas, Hernán, Carlos Buil-Aranda, Aidan Hogan, and Claudia López. "A User Interface for Exploring and Querying Knowledge Graphs (Extended Abstract)." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/666.

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As the adoption of knowledge graphs grows, more and more non-experts users need to be able to explore and query such graphs. These users are not typically familiar with graph query languages such as SPARQL, and may not be familiar with the knowledge graph's structure. In this extended abstract, we provide a summary of our work on a language and visual interface -- called RDF Explorer -- that help non-expert users to navigate and query knowledge graphs. A usability study over Wikidata shows that users successfully complete more tasks with RDF Explorer than with the existing Wikidata Query Helper interface.
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Singer, Uriel, Ido Guy, and Kira Radinsky. "Node Embedding over Temporal Graphs." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/640.

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In this work, we present a method for node embedding in temporal graphs. We propose an algorithm that learns the evolution of a temporal graph's nodes and edges over time and incorporates this dynamics in a temporal node embedding framework for different graph prediction tasks. We present a joint loss function that creates a temporal embedding of a node by learning to combine its historical temporal embeddings, such that it optimizes per given task (e.g., link prediction). The algorithm is initialized using static node embeddings, which are then aligned over the representations of a node at different time points, and eventually adapted for the given task in a joint optimization. We evaluate the effectiveness of our approach over a variety of temporal graphs for the two fundamental tasks of temporal link prediction and multi-label node classification, comparing to competitive baselines and algorithmic alternatives. Our algorithm shows performance improvements across many of the datasets and baselines and is found particularly effective for graphs that are less cohesive, with a lower clustering coefficient.
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Bandeira, Bruno, Márcia R. Cerioli, and Petrucio Viana. "Recognizing which Cographs are Set Graphs." In Encontro de Teoria da Computação. Sociedade Brasileira de Computação - SBC, 2022. http://dx.doi.org/10.5753/etc.2022.223265.

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A set graph is a graph admitting an extensional acyclic orientation. The set graph recognition problem was first considered and proved to be NP-complete by A. Tomescu in 2012. In this work, we introduce two concepts that can be used for the efficient recognition of set graphs in some classes of graphs. We define layered extensional acyclic orientations and a graph parameter, called set-deficiency, that measures how far a graph is from being a set graph. Then, we describe how these concepts can be applied to recognize set graphs in the class of cographs in polynomial time.
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De Silva, K. H. C., and A. A. I. Perera. "Odd Prime Labeling of Snake Graphs." In SLIIT 2nd International Conference on Engineering and Technology. SLIIT, 2023. http://dx.doi.org/10.54389/lufm4069.

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Graph theory is one of the branches of mathematics which is concerned with the networks of points connected by lines. One of the most important research areas in graph theory is graph labeling, which dates back to the 1960s. Graph labeling is assigning integers to the vertices, edges, or both depending on conditions. Labeled graphs are helpful in mathematical models for a wide range of applications such as in coding theory, circuit theory, computer networks, and in cryptography as well. There are various types of graph labeling techniques in graph theory such as radio labeling, graceful labeling, prime labeling, antimagic labeling, and lucky labeling, etc. In this research, we use one of the variations of prime labeling called odd prime labeling of snake graphs. Recent works on odd prime labeling investigate about families of snake graphs, complete graphs, etc and there they discuss about one odd integer sequence only. In this research, we introduce odd prime labeling method for snake graphs for any odd integer sequence and we give a proof for it as well. KEYWORDS: snake graph, odd sequences, odd prime labeling, relatively prime
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Zhang, Ziwei, Xin Wang, and Wenwu Zhu. "Automated Machine Learning on Graphs: A Survey." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/637.

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Machine learning on graphs has been extensively studied in both academic and industry. However, as the literature on graph learning booms with a vast number of emerging methods and techniques, it becomes increasingly difficult to manually design the optimal machine learning algorithm for different graph-related tasks. To solve this critical challenge, automated machine learning (AutoML) on graphs which combines the strength of graph machine learning and AutoML together, is gaining attention from the research community. Therefore, we comprehensively survey AutoML on graphs in this paper, primarily focusing on hyper-parameter optimization (HPO) and neural architecture search (NAS) for graph machine learning. We further overview libraries related to automated graph machine learning and in-depth discuss AutoGL, the first dedicated open-source library for AutoML on graphs. In the end, we share our insights on future research directions for automated graph machine learning. This paper is the first systematic and comprehensive review of automated machine learning on graphs to the best of our knowledge.
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Faria, Luerbio, Mauro Nigro, and Diana Sasaki. "The line graphs of Möbius ladder graphs are Type 1." In Encontro de Teoria da Computação. Sociedade Brasileira de Computação - SBC, 2024. http://dx.doi.org/10.5753/etc.2024.2421.

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A k-total coloring of G is an assignment of k colors to its elements (vertices and edges) such that adjacent or incident elements have distinct colors. The total chromatic number of a graph G is the smallest integer k for which G has a k-total coloring. If the total chromatic number of G is ∆(G) + 1, then we say that G is Type 1. The line graph of G, denoted by L(G), is the graph whose vertex set is the edge set of G and two vertices of the line graph of G are adjacent if the corresponding edges are adjacent in G. In this paper, we prove that the line graphs of Möbius ladder graphs, L(M2n), are Type 1.
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Campos, Raphael R., Ricardo Ferreira, Julio C. Goldner Vendramini, Fábio Cerqueira, and Marcelo Lobato Martins. "Simulation of Scale Free Gene Regulatory Networks based on Threshold Functions on GPU." In Simpósio em Sistemas Computacionais de Alto Desempenho. Sociedade Brasileira de Computação, 2011. http://dx.doi.org/10.5753/wscad.2011.17271.

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Gene regulatory networks have been used to study diseases and cell evolution, where Random Boolean graphs are one of computational approaches. A Boolean graph is a simple and effective model, and its dynamic behavior has been used in several works. This article proposes an efficient environment to simulate Boolean graph on GPU (Graphics Processing Units). The dynamic behavior of a Boolean graph is computed by visiting the whole or a subset of state space. The proposed tool is based on statistical approaches to evaluate large graphs. Moreover, it can take into account scale free graphs with threshold functions. The experimental results show a speed-up factor of up to 40 times. In addition, the exploration of state spaces three orders of magnitude greater than previous approaches have been evaluated.
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Salcedo, Audy, Jesús González, Amalio Sarco LIra, and Johnnalid González. "Statistical Literacy of Citizens: The Interpretation of Statistical Graphs." In Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. International Association for Statistical Education, 2022. http://dx.doi.org/10.52041/iase.icots11.t7a1.

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This article analyzes how a group of Venezuelan citizens interprets two bar graphs. The reading, interpretation and evaluation of statistical graphs is part of the competences that an ordinary citizen must possess. It was therefore decided to ask ordinary citizens to interpret two statistical graphs. The questions are part of a broader questionnaire that was published on the survey administration platform and sent to potential participants, using non-probability sampling. The questions were answered by 407 citizens with different levels of academic training. The results show that most participants gave plausible arguments to support a specific position, but have difficulties in critically evaluating a graph. These results are a first approximation on how Venezuelan citizens interpret statistical graphics and can be a reference for statistical literacy processes.
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Santos, Tanilson D., Jayme Szwarcfiter, Uéverton S. Souza, and Claudson F. Bornstein. "On the Helly Property of Some Intersection Graphs." In Concurso de Teses e Dissertações da SBC. Sociedade Brasileira de Computação, 2021. http://dx.doi.org/10.5753/ctd.2021.15752.

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An EPG graph G is an edge-intersection graph of paths on a grid. In this thesis, we analyze structural characterizations and complexity aspects regarding EPG graphs. Our main focus is on the class of B1-EPG graphs whose intersection model satisfies well-known the Helly property, called Helly-B1-EPG. We show that the problem of recognizing Helly-B1-EPG graphs is NP-complete. Besides, other intersection graph classes such as VPG, EPT, and VPT were also studied. We completely solve the problem of determining the Helly and strong Helly numbers of Bk-EPG graphs and Bk-VPG graphs for each non-negative integer k. Finally, we show that every Chordal B1-EPG graph is at the intersection of VPT and EPT.
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Reports on the topic "Graphs"

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Powers, David. Eigenvectors of Graphs. Fort Belvoir, VA: Defense Technical Information Center, January 1988. http://dx.doi.org/10.21236/ada203317.

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Powers, David L. Eigenvectors of Graphs. Fort Belvoir, VA: Defense Technical Information Center, June 1986. http://dx.doi.org/10.21236/ada170562.

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Dangalchev, Chavdar. Closeness of Splitting Graphs. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, May 2020. http://dx.doi.org/10.7546/crabs.2020.04.03.

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Sanders, G., and R. Pearce. FINAL REPORT: Asynchronous Graphs. Office of Scientific and Technical Information (OSTI), October 2019. http://dx.doi.org/10.2172/1573144.

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Pinter, Michael R. Strongly Well-Covered Graphs. Fort Belvoir, VA: Defense Technical Information Center, January 1993. http://dx.doi.org/10.21236/ada262214.

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Pisan, Yusuf. Visual Reasoning with Graphs. Fort Belvoir, VA: Defense Technical Information Center, January 1994. http://dx.doi.org/10.21236/ada466292.

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Rodger, C. A., D. G. Hoffman, P. D. Johnson, and Jr. Connectivity and Colorings of Graphs. Fort Belvoir, VA: Defense Technical Information Center, March 2002. http://dx.doi.org/10.21236/ada400177.

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Levandoski, J., and G. Abdulla. Temporal Representation in Semantic Graphs. Office of Scientific and Technical Information (OSTI), August 2007. http://dx.doi.org/10.2172/923616.

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Balakirsky, S., and H. Otthein. Planning with incrementally created graphs. Gaithersburg, MD: National Institute of Standards and Technology, 2002. http://dx.doi.org/10.6028/nist.ir.6895.

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Plummer, Michael D. Well-Covered Graphs: A Survey. Fort Belvoir, VA: Defense Technical Information Center, January 1991. http://dx.doi.org/10.21236/ada247861.

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