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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"

1

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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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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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 tu

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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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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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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 automorp

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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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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 alg

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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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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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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

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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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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

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Дисертації з теми "Automorphisme des graphes"

1

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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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 carac

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2

Aurand, Eric William. "Infinite Planar Graphs." Thesis, University of North Texas, 2000. https://digital.library.unt.edu/ark:/67531/metadc2545/.

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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 identi

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3

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 numb

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4

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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5

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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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

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6

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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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 sta

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7

Hahn, Gena. "Sur des graphes finis et infinis." Paris 11, 1986. http://www.theses.fr/1986PA112166.

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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 refroidisseme

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8

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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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

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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 g

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10

Allie, Imran. "Meta-Cayley Graphs on Dihedral Groups." University of the Western Cape, 2017. http://hdl.handle.net/11394/5440.

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>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 de

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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 transtempo

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