Готові списки джерел за темами / Automorphisme des graphes

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Добірка наукової літератури з теми "Automorphisme des graphes"

Автор: Grafiati
Опубліковано: 20 квітня 2024

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Статті в журналах з теми "Automorphisme des graphes"

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Kutnar, Klavdija, Dragan Marusic, Stefko Miklavic, and Rok Strasek. "Automorphisms of Tabacjn graphs." Filomat 27, no. 7 (2013): 1157–64. http://dx.doi.org/10.2298/fil1307157k.

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Анотація:
A bicirculant is a graph admitting an automorphism whose cyclic decomposition consists of two cycles of equal length. In this paper we consider automorphisms of the so-called Tahacjn graphs, a family of pentavalent bicirculants which are obtained from the generalized Petersen graphs by adding two additional perfect matchings between the two orbits of the above mentioned automorphism. As a corollary, we determine which Tabacjn graphs are vertex-transitive.
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2

Della-Giustina, James. "Finding the Fixing Number of Johnson Graphs J(n, k) for k Є {2; 3}". American Journal of Undergraduate Research 20, № 3 (2023): 81–89. http://dx.doi.org/10.33697/ajur.2023.097.

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Анотація:
The graph invariant, aptly named the fixing number, is the smallest number of vertices that, when fixed, eliminate all non-trivial automorphisms (or symmetries) of a graph. Although many graphs have established fixing numbers, Johnson graphs, a family of graphs related to the graph isomorphism problem, have only partially classified fixing numbers. By examining specific orbit sizes of the automorphism group of Johnson graphs and classifying the subsequent remaining subgroups of the automorphism group after iteratively fixing vertices, we provide exact minimal sequences of fixed vertices, in turn establishing the fixing number of infinitely many Johnson graphs. KEYWORDS: Graph Automorphism Groups; Symmetry Breaking; Fixing Number; Determining Number; Johnson Graphs; Kneser Graphs; Graph Invariants; Permutation Groups; Minimal Sized Bases.
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3

Ghorbani, Modjtaba, Matthias Dehmer, Abbe Mowshowitz, Jin Tao, and Frank Emmert-Streib. "The Hosoya Entropy of Graphs Revisited." Symmetry 11, no. 8 (2019): 1013. http://dx.doi.org/10.3390/sym11081013.

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Анотація:
In this paper we extend earlier results on Hosoya entropy (H-entropy) of graphs, and establish connections between H-entropy and automorphisms of graphs. In particular, we determine the H-entropy of graphs whose automorphism group has exactly two orbits, and characterize some classes of graphs with zero H-entropy.
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4

Maksimović, Marija. "On Some Regular Two-Graphs up to 50 Vertices." Symmetry 15, no. 2 (2023): 408. http://dx.doi.org/10.3390/sym15020408.

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Анотація:
Regular two-graphs on up to 36 vertices are classified, and recently, the classification of regular two-graphs on 38 and 42 vertices having at least one descendant with a nontrivial automorphism group has been performed. The first unclassified cases are those on 46 and 50 vertices. It is known that there are at least 97 regular two-graphs on 46 vertices leading to 2104 descendants and 54 regular two-graphs on 50 vertices leading to 785 descendants. In this paper, we classified all strongly regular graphs with parameters (45,22,10,11), (49,24,11,12), and (50,21,8,9) that have Z6 as the automorphism group and constructed regular two-graphs from SRGs (45,22,10,11), SRGs (49,24,11,12), and SRGs (50,21,8,9) that have automorphisms of order six. In this way, we enumerated all regular two-graphs on up to 50 vertices that have at least one descendant with an automorphism group of order six or at least one strongly regular graph associated with an automorphism group of order six. We found 236 new regular two-graphs on 46 vertices leading to 3172 new SRG (45,22,10,11) and 51 new regular two-graphs on 50 vertices leading to 398 new SRG (49,24,11,12).
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5

Łuczak, Tomasz. "The automorphism group of random graphs with a given number of edges." Mathematical Proceedings of the Cambridge Philosophical Society 104, no. 3 (1988): 441–49. http://dx.doi.org/10.1017/s0305004100065646.

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Анотація:
An automorphism σ(G) of a graph G is a permutation of the set of its vertices which preserves adjacency. Under the operation of composition the automorphisms of G form a group Aut(G). The graph G is called asymmetric if Aut(G) is trivial, and symmetric otherwise.
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6

Hernández-Gómez, Juan C., Gerardo Reyna-Hérnandez, Jesús Romero-Valencia, and Omar Rosario Cayetano. "Transitivity on Minimum Dominating Sets of Paths and Cycles." Symmetry 12, no. 12 (2020): 2053. http://dx.doi.org/10.3390/sym12122053.

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Анотація:
Transitivity on graphs is a concept widely investigated. This suggest to analyze the action of automorphisms on other sets. In this paper, we study the action on the family of γ-sets (minimum dominating sets), the graph is called γ-transitive if given two γ-sets there exists an automorphism which maps one onto the other. We deal with two families: paths Pn and cycles Cn. Their γ-sets are fully characterized and the action of the automorphism group on the family of γ-sets is fully analyzed.
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7

Ball, Fabian, and Andreas Geyer-Schulz. "Invariant Graph Partition Comparison Measures." Symmetry 10, no. 10 (2018): 504. http://dx.doi.org/10.3390/sym10100504.

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Анотація:
Symmetric graphs have non-trivial automorphism groups. This article starts with the proof that all partition comparison measures we have found in the literature fail on symmetric graphs, because they are not invariant with regard to the graph automorphisms. By the construction of a pseudometric space of equivalence classes of permutations and with Hausdorff’s and von Neumann’s methods of constructing invariant measures on the space of equivalence classes, we design three different families of invariant measures, and we present two types of invariance proofs. Last, but not least, we provide algorithms for computing invariant partition comparison measures as pseudometrics on the partition space. When combining an invariant partition comparison measure with its classical counterpart, the decomposition of the measure into a structural difference and a difference contributed by the group automorphism is derived.
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8

FERN, LORI, GARY GORDON, JASON LEASURE, and SHARON PRONCHIK. "Matroid Automorphisms and Symmetry Groups." Combinatorics, Probability and Computing 9, no. 2 (2000): 105–23. http://dx.doi.org/10.1017/s0963548399004125.

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Анотація:
For a subgroup W of the hyperoctahedral group On which is generated by reflections, we consider the linear dependence matroid MW on the column vectors corresponding to the reflections in W. We determine all possible automorphism groups of MW and determine when W ≅ = Aut(MW). This allows us to connect combinatorial and geometric symmetry. Applications to zonotopes are also considered. Signed graphs are used as a tool for constructing the automorphisms.
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9

Moreira de Oliveira, Montauban, and Jean-Guillaume Eon. "Non-crystallographic nets: characterization and first steps towards a classification." Acta Crystallographica Section A Foundations and Advances 70, no. 3 (2014): 217–28. http://dx.doi.org/10.1107/s2053273314000631.

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Анотація:
Non-crystallographic (NC) nets are periodic nets characterized by the existence of non-trivial bounded automorphisms. Such automorphisms cannot be associated with any crystallographic symmetry in realizations of the net by crystal structures. It is shown that bounded automorphisms of finite order form a normal subgroupF(N) of the automorphism group of NC nets (N,T). As a consequence, NC nets are unstable nets (they display vertex collisions in any barycentric representation) and, conversely, stable nets are crystallographic nets. The labelled quotient graphs of NC nets are characterized by the existence of an equivoltage partition (a partition of the vertex set that preserves label vectors over edges between cells). A classification of NC nets is proposed on the basis of (i) their relationship to the crystallographic net with a homeomorphic barycentric representation and (ii) the structure of the subgroupF(N).
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10

Tsiovkina, Ludmila Yu. "ON A CLASS OF EDGE-TRANSITIVE DISTANCE-REGULAR ANTIPODAL COVERS OF COMPLETE GRAPHS." Ural Mathematical Journal 7, no. 2 (2021): 136. http://dx.doi.org/10.15826/umj.2021.2.010.

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Анотація:
The paper is devoted to the problem of classification of edge-transitive distance-regular antipodal covers of complete graphs. This extends the classification of those covers that are arc-transitive, which has been settled except for some tricky cases that remain to be considered, including the case of covers satisfying condition \(c_2=1\) (which means that every two vertices at distance 2 have exactly one common neighbour).Here it is shown that an edge-transitive distance-regular antipodal cover of a complete graph with \(c_2=1\) is either the second neighbourhood of a vertex in a Moore graph of valency 3 or 7, or a Mathon graph, or a half-transitive graph whose automorphism group induces an affine \(2\)-homogeneous group on the set of its fibres. Moreover, distance-regular antipodal covers of complete graphs with \(c_2=1\) that admit an automorphism group acting \(2\)-homogeneously on the set of fibres (which turns out to be an approximation of the property of edge-transitivity of such cover), are described. A well-known correspondence between distance-regular antipodal covers of complete graphs with \(c_2=1\) and geodetic graphs of diameter two that can be viewed as underlying graphs of certain Moore geometries, allows us to effectively restrict admissible automorphism groups of covers under consideration by combining Kantor's classification of involutory automorphisms of these geometries together with the classification of finite 2-homogeneous permutation groups.
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Дисертації з теми "Automorphisme des graphes"

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Carboni, Lucrezia. "Graphes pour l’exploration des réseaux de neurones artificiels et de la connectivité cérébrale humaine." Electronic Thesis or Diss., Université Grenoble Alpes, 2023. http://www.theses.fr/2023GRALM060.

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Анотація:
L'objectif principal de cette thèse est d'explorer la connectivité cérébrale et celle des réseaux de neurones artificiels d'un point de vue de leur connectivité. Un modèle par graphes pour l'analyse de la connectivité structurelle et fonctionnelle a été largement étudié dans le contexte du cerveau humain mais, un tel cadre d'analyse manque encore pour l'analyse des systèmes artificiels. Avec l'objectif d'intégrer l'analyse de la connectivité dans les système artificiels, cette recherche se concentre sur deux axes principaux. Dans le premier axe, l'objectif principal est de déterminer une caractérisation de la signature saine de la connectivité fonctionnelle de repos du cerveau humain. Pour atteindre cet objectif, une nouvelle méthode est proposée, intégrant des statistiques de graphe traditionnelles et des outils de réduction de réseau, pour déterminer des modèles de connectivité sains. Ainsi, nous construisons une comparaison en paires de graphes et un classifieur pour identifier les états pathologiques et identifier les régions cérébrales perturbées par une pathologie. De plus, la généralisation et la robustesse de la méthode proposée ont été étudiées sur plusieurs bases de données et variations de la qualité des données. Le deuxième axe de recherche explore les avantages de l'intégration des études de la connectivité inspirée du cerveau aux réseaux de neurones artificiels (ANNs) dans la perspective du développement de systèmes artificiels plus robustes. Un problème majeur de robustesse dans les modèles d'ANN est représenté par l'oubli catastrophique qui apparaît lorsque le réseau oublie dramatiquement les tâches précédemment apprises lors de l'adaptation à de nouvelles tâches. Notre travail démontre que la modélisation par graphes offre un cadre simple et élégant pour étudier les ANNs, comparer différentes stratégies d'apprentissage et détecter des comportements nuisibles tels que l'oubli catastrophique. De plus, nous soulignons le potentiel d'une adaptation à de nouvelles tâches en contrôlant les graphes afin d'atténuer efficacement l'oubli catastrophique et jetant ainsi les bases de futures recherches et explorations dans ce domaine<br>The main objective of this thesis is to explore brain and artificial neural network connectivity from agraph-based perspective. While structural and functional connectivity analysis has been extensivelystudied in the context of the human brain, there is a lack of a similar analysis framework in artificialsystems.To address this gap, this research focuses on two main axes.In the first axis, the main objective is to determine a healthy signature characterization of the humanbrain resting state functional connectivity. To achieve this objective, a novel framework is proposed,integrating traditional graph statistics and network reduction tools, to determine healthy connectivitypatterns. Hence, we build a graph pair-wise comparison and a classifier to identify pathological statesand rank associated perturbed brain regions. Additionally, the generalization and robustness of theproposed framework were investigated across multiple datasets and variations in data quality.The second research axis explores the benefits of brain-inspired connectivity exploration of artificialneural networks (ANNs) in the future perspective of more robust artificial systems development. Amajor robustness issue in ANN models is represented by catastrophic forgetting when the networkdramatically forgets previously learned tasks when adapting to new ones. Our work demonstrates thatgraph modeling offers a simple and elegant framework for investigating ANNs, comparing differentlearning strategies, and detecting deleterious behaviors such as catastrophic forgetting.Moreover, we explore the potential of leveraging graph-based insights to effectively mitigatecatastrophic forgetting, laying a foundation for future research and explorations in this area
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Aurand, Eric William. "Infinite Planar Graphs." Thesis, University of North Texas, 2000. https://digital.library.unt.edu/ark:/67531/metadc2545/.

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Анотація:
How many equivalence classes of geodesic rays does a graph contain? How many bounded automorphisms does a planar graph have? Neimayer and Watkins studied these two questions and answered them for a certain class of graphs. Using the concept of excess of a vertex, the class of graphs that Neimayer and Watkins studied are extended to include graphs with positive excess at each vertex. The results of this paper show that there are an uncountable number of geodesic fibers for graphs in this extended class and that for any graph in this extended class the only bounded automorphism is the identity automorphism.
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Derakhshan, Parisa. "Automorphisms generating disjoint Hamilton cycles in star graphs." Thesis, Loughborough University, 2015. https://dspace.lboro.ac.uk/2134/16779.

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Анотація:
In the first part of the thesis we define an automorphism φn for each star graph Stn of degree n-1, which yields permutations of labels for the edges of Stn taken from the set of integers {1,..., [n/2c]}. By decomposing these permutations into permutation cycles, we are able to identify edge-disjoint Hamilton cycles that are automorphic images of a known two-labelled Hamilton cycle H1 2(n) in Stn. The search for edge-disjoint Hamilton cycles in star graphs is important for the design of interconnection network topologies in computer science. All our results improve on the known bounds for numbers of any kind of edge-disjoint Hamilton cycles in star graphs.
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Schmidt, Simon [Verfasser]. "Quantum automorphism groups of finite graphs / Simon Schmidt." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2020. http://d-nb.info/1216104816/34.

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Crinion, Tim. "Chamber graphs of some geometries related to the Petersen graph." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/chamber-graphs-of-some-geometries-related-to-the-petersen-graph(f481f0af-7c39-4728-8928-571495d1217a).html.

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Анотація:
In this thesis we study the chamber graphs of the geometries ΓpA2nΓ1q, Γp3A7q, ΓpL2p11qq and ΓpL2p25qq which are related to the Petersen graph [4, 13]. In Chapter 2 we look at the chamber graph of ΓpA2nΓ1q and see what minimal paths between chambers look like. Chapter 3 finds and proves the diameter of these chamber graphs and we see what two chambers might look like if they are as far apart as possible. We discover the full automorphism group of the chamber graph. Chapters 4, 5 and 6 focus on the chamber graphs of ΓpL2p11qq,ΓpL2p25qq and Γp3A7q respectively. We ask questions such as what two chambers look like if they are as far apart as possible, and we find the automorphism groups of the chamber graphs.
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Möller, Rögnvaldur G. "Groups acting on graphs." Thesis, University of Oxford, 1991. http://ora.ox.ac.uk/objects/uuid:2dacfc67-56c4-4541-b52e-10199a13dcc2.

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Анотація:
In the first part of this thesis we investigate the automorphism groups of regular trees. In the second part we look at the action of the automorphism group of a locally finite graph on the ends of the graph. The two part are not directly related but trees play a fundamental role in both parts. Let T<sub>n</sub> be the regular tree of valency n. Put G := Aut(T<sub>n</sub>) and let G<sub>0</sub> be the subgroup of G that is generated by the stabilisers of points. The main results of the first part are : Theorem 4.1 Suppose 3 ≤ n < N<sub>0</sub> and α ϵ T<sub>n</sub>. Then G<sub>α</sub> (the stabiliser of α in G) contains 2<sup>2N0</sup> subgroups of index less than 2<sup>2N0</sup>. Theorem 4.2 Suppose 3 ≤ n < N<sub>0</sub> and H ≤ G with G : H |< 2<sup>N0</sup>. Then H = G or H = G<sub>0</sub> or H fixes a point or H stabilises an edge. Theorem 4.3 Let n = N<sub>0</sub> and H ≤ G with | G : H |< 2<sup>N0</sup>. Then H = G or H = G<sub>0</sub> or there is a finite subtree ϕ of T<sub>n</sub> such that G(<sub>ϕ</sub>) ≤ H ≤ G{<sub>ϕ</sub>}. These are proved by finding a concrete description of the stabilisers of points in G, using wreath products, and also by making use of methods and results of Dixon, Neumann and Thomas [Bull. Lond. Math. Soc. 18, 580-586]. It is also shown how one is able to get short proofs of three earlier results about the automorphism groups of regular trees by using the methods used to prove these theorems. In their book Groups acting on graphs, Warren Dicks and M. J. Dunwoody [Cambridge University Press, 1989] developed a powerful technique to construct trees from graphs. An end of a graph is an equivalence class of half-lines in the graph, with two half-lines, L<sub>1</sub> and L<sub>2</sub>, being equivalent if and only if we can find the third half-line that contains infinitely many vertices of both L<sub>1</sub> and L<sub>2</sub>. In the second part we point out how one can, by using this technique, reduce questions about ends of graphs to questions about trees. This allows us both to prove several new results and also to give simple proofs of some known results concerning fixed points of group actions on the ends of a locally finite graph (see Chapter 10). An example of a new result is the classification of locally finite graphs with infinitely many ends, whose automorphism group acts transitively on the set of ends (Theorem 11.1).
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Hahn, Gena. "Sur des graphes finis et infinis." Paris 11, 1986. http://www.theses.fr/1986PA112166.

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Анотація:
Ce travail porte sur l'étude des relations entre la microstructure et paramètres d'élaboration des rubans de l'alliage binaire Al-8% Fe. Les paramètres étudiés sont entre autres : - pression d'éjection et vitesse du substrat, -nature et rugosité du substrat,- température d'éjection. La microstructure des rubans élaborés en jet libre est classée en trois familles : structure de solidification micro-cellulaire, dendritique et équiaxe contenant des précipités. Nous montrons qu'il est possible d'éviter la formation de la structure dendritique grossière correspondant aux conditions de refroidissement les plus lentes : toutefois, les caractéristiques morphologiques des rubans ainsi qu'un bon contact thermique entre celui-ci et le substrat sont à rechercher. Nous en déduisons que la mouillabilité de l'alliage liquide sur le substrat est le critère le plus important et l'influence des paramètres d'élaboration est discuté en termes de distance de collage des rubans sur le substrat. L'élaboration de rubans en jet confiné est également étudiée et leur microstructure est comparée à celle de leurs homologues élaborés en jet libre<br>This work describes the dependence of microstructural features on rapid solidification processing for the melt spun Al-8% Fe alloy. The inspected parameters are: - ejection pressure and substrate velocity, - nature and rugosity of susbtrate, - ejection temperature. The resultant microstructures of the chill block melt spun ribbons is classified into three families: micro-cellular and dendritic structures, and equiaxed grains containing precipitates. It is possible to avoid the occurrence of the coarse dendritic structure corresponding to the slowest cooling conditions however, uniformity of the ribbon morphologic characteristics and good thermal contact between the ribbon and the weel have to be insured. So, improvement of wetting is the major point. The influence of process parameters on wetting is discussed and particular attention is paid to the sticking distance between the ribbon and the substrate. The planar flow casting method has been developed and microstructural results are compared to those given by the C. B. M. S. Technique
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Bougard, Nicolas. "Regular graphs and convex polyhedra with prescribed numbers of orbits." Doctoral thesis, Universite Libre de Bruxelles, 2007. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210688.

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Анотація:
Etant donné trois entiers k, s et a, nous prouvons dans le premier chapitre qu'il existe un graphe k-régulier fini (resp. un graphe k-régulier connexe fini) dont le groupe d'automorphismes a exactement s orbites sur l'ensemble des sommets et a orbites sur l'ensemble des arêtes si et seulement si<p><p>(s,a)=(1,0) si k=0,<p>(s,a)=(1,1) si k=1,<p>s=a>0 si k=2,<p>0< s <= 2a <= 2ks si k>2.<p><p>(resp.<p>(s,a)=(1,0) si k=0,<p>(s,a)=(1,1) si k=1 ou 2,<p>s-1<=a<=(k-1)s+1 et s,a>0 si k>2.)<p><p>Nous étudions les polyèdres convexes de R³ dans le second chapitre. Pour tout polyèdre convexe P, nous notons Isom(P) l'ensemble des isométries de R³ laissant P invariant. Si G est un sous-groupe de Isom(P), le f_G-vecteur de P est le triple d'entiers (s,a,f) tel que G ait exactement s orbites sur l'ensemble sommets de P, a orbites sur l'ensemble des arêtes de P et f orbites sur l'ensemble des faces de P. Remarquons que (s,a,f) est le f_{id}-vecteur (appelé f-vecteur dans la littérature) d'un polyèdre si ce dernier possède exactement s sommets, a arêtes et f faces. Nous généralisons un théorème de Steinitz décrivant tous les f-vecteurs possibles. Pour tout groupe fini G d'isométries de R³, nous déterminons l'ensemble des triples (s,a,f) pour lesquels il existe un polyèdre convexe ayant (s,a,f) comme f_G-vecteur. Ces résultats nous permettent de caractériser les triples (s,a,f) pour lesquels il existe un polyèdre convexe tel que Isom(P) a s orbites sur l'ensemble des sommets, a orbites sur l'ensemble des arêtes et f orbites sur l'ensemble des faces.<p><p>La structure d'incidence I(P) associée à un polyèdre P consiste en la donnée de l'ensemble des sommets de P, l'ensemble des arêtes de P, l'ensemble des faces de P et de l'inclusion entre ces différents éléments (la notion de distance ne se trouve pas dans I(P)). Nous déterminons également l'ensemble des triples d'entiers (s,a,f) pour lesquels il existe une structure d'incidence I(P) associée à un polyèdre P dont le groupe d'automorphismes a exactement s orbites de sommets, a orbites d'arêtes et f orbites de sommets.<br>Doctorat en sciences, Spécialisation mathématiques<br>info:eu-repo/semantics/nonPublished
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9

Adatorwovor, Dayana. "H - Removable Sequences of Graphs." OpenSIUC, 2014. https://opensiuc.lib.siu.edu/dissertations/791.

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Анотація:
H-removable sequences, for arbitrary H, under &Lambda^* construction are presented here. In the first part we investigate Neighborhood Distinct (ND) graphs and ask some natural questions concerning disconnected H and H complement. In the second part, we introduce property * and investigate graphs that satisfy property *. Consequently we find $H$-removable sequences for all graphs H with up to 6 vertices except for G60. G60 is the only graph with up to 6 vertices for which neither it nor its complement satisfies property *. The last part of our work focuses on good and bad copies of arbitrary graphs $H$ and how to interchange from one to the other. The number of ways to count all possible copies of H in H_{pn} ^ &Lambda^* is also presented via examples.
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Allie, Imran. "Meta-Cayley Graphs on Dihedral Groups." University of the Western Cape, 2017. http://hdl.handle.net/11394/5440.

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Анотація:
>Magister Scientiae - MSc<br>The pursuit of graphs which are vertex-transitive and non-Cayley on groups has been ongoing for some time. There has long been evidence to suggest that such graphs are a very rarety in occurrence. Much success has been had in this regard with various approaches being used. The aim of this thesis is to find such a class of graphs. We will take an algebraic approach. We will define Cayley graphs on loops, these loops necessarily not being groups. Specifically, we will define meta-Cayley graphs, which are vertex-transitive by construction. The loops in question are defined as the semi-direct product of groups, one of the groups being Z₂ consistently, the other being in the class of dihedral groups. In order to prove non-Cayleyness on groups, we will need to fully determine the automorphism groups of these graphs. Determining the automorphism groups is at the crux of the matter. Once these groups are determined, we may then apply Sabidussi's theorem. The theorem states that a graph is Cayley on groups if and only if its automorphism group contains a subgroup which acts regularly on its vertex set.<br>Chemicals Industries Education and Training Authority (CHIETA)
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Книги з теми "Automorphisme des graphes"

1

The classification of minimal graphs with given abelian automorphism group. American Mathematical Society, 1985.

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2

Rubin, Matatyahu. The reconstruction of trees from their automorphism groups. American Mathematical Society, 1993.

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3

Goodman, Albert J. Automorphism groups of graphs: Asymptotic problems. 1992.

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4

Lauri, Josef, and Raffaele Scapellato. Topics in Graph Automorphisms and Reconstruction. Cambridge University Press, 2016.

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5

Lauri, Josef, and Raffaele Scapellato. Topics in Graph Automorphisms and Reconstruction (London Mathematical Society Student Texts). Cambridge University Press, 2003.

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6

Lauri, Josef, and Raffaele Scapellato. Topics in Graph Automorphisms and Reconstruction. Cambridge University Press, 2016.

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7

Lauri, Josef, and Raffaele Scapellato. Topics in Graph Automorphisms and Reconstruction. Cambridge University Press, 2016.

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8

Lauri, Josef, and Raffaele Scapellato. Topics in Graph Automorphisms and Reconstruction (London Mathematical Society Student Texts). Cambridge University Press, 2003.

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Частини книг з теми "Automorphisme des graphes"

1

Bretto, Alain, Alain Faisant, and François Hennecart. "Automorphismes — Théorie spectrale." In Éléments de théorie des graphes. Springer Paris, 2012. http://dx.doi.org/10.1007/978-2-8178-0281-7_9.

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2

Watkins, Mark E. "Ends and automorphisms of infinite graphs." In Graph Symmetry. Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-015-8937-6_9.

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3

Baumann, U., M. Lesch, and I. Schmeichel. "Automorphism Groups of Directed Cayley Graphs." In Topics in Combinatorics and Graph Theory. Physica-Verlag HD, 1990. http://dx.doi.org/10.1007/978-3-642-46908-4_14.

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4

Hong, Seok-Hee, Peter Eades, and Sang-Ho Lee. "Finding Planar Geometric Automorphisms in Planar Graphs." In Algorithms and Computation. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/3-540-49381-6_30.

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5

Faradžev, I. A., M. H. Klin, and M. E. Muzichuk. "Cellular Rings and Groups of Automorphisms of Graphs." In Investigations in Algebraic Theory of Combinatorial Objects. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-017-1972-8_1.

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6

Muzychuk, M. E. "Automorphism Groups of Paley Graphs and Cyclotomic Schemes." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-32808-5_6.

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7

Harvey, W. J. "Discrete Groups and Surface Automorphisms: A Theorem of A.M. Macbeath." In Symmetries in Graphs, Maps, and Polytopes. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-30451-9_9.

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8

Polak, Monika, and Vasyl Ustimenko. "On LDPC Codes Based on Families of Expanding Graphs of Increasing Girth without Edge-Transitive Automorphism Groups." In Communications in Computer and Information Science. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-44893-9_7.

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9

Clay, Matt. "Automorphisms of Free Groups." In Office Hours with a Geometric Group Theorist. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691158662.003.0006.

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Анотація:
This chapter discusses the automorphisms of free groups. Every group is the collection of symmetries of some object, namely, its Cayley graph. A symmetry of a group is called an automorphism; it is merely an isomorphism of the group to itself. The collection of all of the automorphisms is also a group too, known as the automorphism group and denoted by Aut (G). The chapter considers basic examples of groups to illustrate what an automorphism is, with a focus on the automorphisms of the symmetric group on three elements and of the free abelian group. It also examines the dynamics of an automorphism of a free group and concludes with a description of train tracks, a topological model for the free group, and the Perron–Frobenius theorem. Exercises and research projects are included.
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10

Cameron, Peter J. "Groups." In Graph Connections. Oxford University PressOxford, 1997. http://dx.doi.org/10.1093/oso/9780198514978.003.0009.

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Abstract In this chapter, the connections between a graph and its automorphism group are described. The main themes are that most graphs have very little symmetry; abstract automorphism groups can be prescribed independently of most graph- theoretic properties; vertex-transitivity, however, entails various structural properties; and still higher degrees of symmetry can be expected to lead to a complete classification. The most important connection between graphs and groups is the fact that every graph G has an automorphism group, consisting of all permutations of the vertex set which map edges to edges and non-edges to non-edges. For most graphs, the automorphism group is trivial, consisting of only the identity permutation. However, every group is the automorphism group of some graph, and highly symmetric graphs have a number of special properties not shared by arbitrary graphs.
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Тези доповідей конференцій з теми "Automorphisme des graphes"

1

Molchanov, Vladimir Alexandrovich, and Renat Abuhanovich Farakhutdinov. "Structure of isomrphisms and automorphism groups of universal graph automata." In Academician O.B. Lupanov 14th International Scientific Seminar "Discrete Mathematics and Its Applications". Keldysh Institute of Applied Mathematics, 2022. http://dx.doi.org/10.20948/dms-2022-63.

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The paper studies graph automata, the set of states and the set whose output signals are endowed with graph structures. Universal graph automata are universally attracting objects in categories of semigroup graph automata. In this work a description of the structure of isomorphisms and automorphism groups of such automata and their connection with isomorphisms and automorphism groups machine component.
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2

Babai, László. "On the automorphism groups of strongly regular graphs I." In ITCS'14: Innovations in Theoretical Computer Science. ACM, 2014. http://dx.doi.org/10.1145/2554797.2554830.

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3

Salat, Arti, and Amit Sharma. "Automorphism groups and distinguishing numbers of some graphs related to cycle graph." In 2ND INTERNATIONAL CONFERENCE ON APPLIED MATHEMATICS AND COMPUTATIONAL SCIENCES 2022 (ICAMCS-2022). AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0199429.

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4

Abrahão, Felipe, Klaus Wehmuth, and Artur Ziviani. "Transtemporal edges and crosslayer edges in incompressible high-order networks." In IV Encontro de Teoria da Computação. Sociedade Brasileira de Computação - SBC, 2019. http://dx.doi.org/10.5753/etc.2019.6389.

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This work presents some outcomes of a theoretical investigation of incompressible high-order networks defined by a generalized graph represen tation. We study some of their network topological properties and how these may be related to real world complex networks. We show that these networks have very short diameter, high k-connectivity, degrees of the order of half of the network size within a strong-asymptotically dominated standard deviation, and rigidity with respect to automorphisms. In addition, we demonstrate that incompressible dynamic (or dynamic multilayered) networks have transtemporal (or crosslayer) edges and, thus, a snapshot-like representation of dynamic networks is inaccurate for capturing the presence of such edges that compose underlying structures of some real-world networks.
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