Relevant bibliographies by topics / Symmetries of vertex-transitive

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Academic literature on the topic 'Symmetries of vertex-transitive'

Author: Grafiati
Published: 4 June 2021
Last updated: 19 February 2022

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Journal articles on the topic "Symmetries of vertex-transitive"

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ALAEIYAN, MEHDI, and MOHSEN GHASEMI. "CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 8p2." Bulletin of the Australian Mathematical Society 77, no. 2 (2008): 315–23. http://dx.doi.org/10.1017/s0004972708000361.

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AbstractA simple undirected graph is said to be semisymmetric if it is regular and edge-transitive but not vertex-transitive. Let p be a prime. It was shown by Folkman [J. Folkman, ‘Regular line-symmetric graphs’, J. Combin. Theory3 (1967), 215–232] that a regular edge-transitive graph of order 2p or 2p2 is necessarily vertex-transitive. In this paper an extension of his result in the case of cubic graphs is given. It is proved that every cubic edge-transitive graph of order 8p2 is vertex-transitive.
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Hua, Xiao-Hui, and Yan-Quan Feng. "Cubic graphs admitting transitive non-abelian characteristically simple groups." Proceedings of the Edinburgh Mathematical Society 54, no. 1 (2011): 113–23. http://dx.doi.org/10.1017/s0013091509000625.

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AbstractLet Γ be a graph and let G be a vertex-transitive subgroup of the full automorphism group Aut(Γ) of Γ. The graph Γ is called G-normal if G is normal in Aut(Γ). In particular, a Cayley graph Cay(G, S) on a group G with respect to S is normal if the Cayley graph is R(G)-normal, where R(G) is the right regular representation of G. Let T be a non-abelian simple group and let G = Tℓ with ℓ ≥ 1. We prove that if every connected T-vertex-transitive cubic symmetric graph is T-normal, then every connected G-vertex-transitive cubic symmetric graph is G-normal. This result, among others, implies
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REZA SALARIAN, M. "FINITE SYMMETRIC GRAPHS WITH 2-ARC-TRANSITIVE QUOTIENTS: AFFINE CASE." Bulletin of the Australian Mathematical Society 93, no. 1 (2015): 13–18. http://dx.doi.org/10.1017/s0004972715000970.

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Let $G$ be a finite group and ${\rm\Gamma}$ a $G$-symmetric graph. Suppose that $G$ is imprimitive on $V({\rm\Gamma})$ with $B$ a block of imprimitivity and ${\mathcal{B}}:=\{B^{g};g\in G\}$ a system of imprimitivity of $G$ on $V({\rm\Gamma})$. Define ${\rm\Gamma}_{{\mathcal{B}}}$ to be the graph with vertex set ${\mathcal{B}}$ such that two blocks $B,C\in {\mathcal{B}}$ are adjacent if and only if there exists at least one edge of ${\rm\Gamma}$ joining a vertex in $B$ and a vertex in $C$. Xu and Zhou [‘Symmetric graphs with 2-arc-transitive quotients’, J. Aust. Math. Soc. 96 (2014), 275–288]
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HAMIDOUNE, YAHYA OULD. "On Iterated Image Size for Point-Symmetric Relations." Combinatorics, Probability and Computing 17, no. 1 (2008): 61–66. http://dx.doi.org/10.1017/s0963548307008620.

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Let Γ =(V,E) be a point-symmetric reflexive relation and let υ ∈ V such that |Γ(υ)| is finite (and hence |Γ(x)| is finite for all x, by the transitive action of the group of automorphisms). Let j ∈ℕ be an integer such that Γj(υ)∩ Γ−(υ)={υ}. Our main result states that As an application we have |Γj(υ)| ≥ 1+(|Γ(υ)|−1)j. The last result confirms a recent conjecture of Seymour in the case of vertex-symmetric graphs. Also it gives a short proof for the validity of the Caccetta–Häggkvist conjecture for vertex-symmetric graphs and generalizes an additive result of Shepherdson.
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Ashari, Yeva Fadhilah, A. N. M. Salman, and Rinovia Simanjuntak. "On Forbidden Subgraphs of (K2, H)-Sim-(Super)Magic Graphs." Symmetry 13, no. 8 (2021): 1346. http://dx.doi.org/10.3390/sym13081346.

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A graph G admits an H-covering if every edge of G belongs to a subgraph isomorphic to a given graph H. G is said to be H-magic if there exists a bijection f:V(G)∪E(G)→{1,2,…,|V(G)|+|E(G)|} such that wf(H′)=∑v∈V(H′)f(v)+∑e∈E(H′)f(e) is a constant, for every subgraph H′ isomorphic to H. In particular, G is said to be H-supermagic if f(V(G))={1,2,…,|V(G)|}. When H is isomorphic to a complete graph K2, an H-(super)magic labeling is an edge-(super)magic labeling. Suppose that G admits an F-covering and H-covering for two given graphs F and H. We define G to be (F,H)-sim-(super)magic if there exists
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Ma, Xuesong, and Ruji Wang. "Trivalent Non-symmetric Vertex-Transitive Graphs of Order at Most 150." Algebra Colloquium 15, no. 03 (2008): 379–90. http://dx.doi.org/10.1142/s1005386708000370.

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Let X be a simple undirected connected trivalent graph. Then X is said to be a trivalent non-symmetric graph of type (II) if its automorphism group A = Aut (X) acts transitively on the vertices and the vertex-stabilizer Av of any vertex v has two orbits on the neighborhood of v. In this paper, such graphs of order at most 150 with the basic cycles of prime length are investigated, and a classification is given for such graphs which are non-Cayley graphs, whose block graphs induced by the basic cycles are non-bipartite graphs.
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Du, Jiali, Yanquan Feng, and Yuqin Liu. "Heptavalent Symmetric Graphs with Certain Conditions." Algebra Colloquium 28, no. 02 (2021): 243–52. http://dx.doi.org/10.1142/s1005386721000195.

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A graph [Formula: see text] is said to be symmetric if its automorphism group [Formula: see text] acts transitively on the arc set of [Formula: see text]. We show that if [Formula: see text] is a finite connected heptavalent symmetric graph with solvable stabilizer admitting a vertex-transitive non-abelian simple group [Formula: see text] of automorphisms, then either [Formula: see text] is normal in [Formula: see text], or [Formula: see text] contains a non-abelian simple normal subgroup [Formula: see text] such that [Formula: see text] and [Formula: see text] is explicitly given as one of 11
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Stojanovic, Milica. "Coxeter groups as automorphism groups of solid transitive 3-simplex tilings." Filomat 28, no. 3 (2014): 557–77. http://dx.doi.org/10.2298/fil1403557s.

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In the papers of I.K. Zhuk, then more completely of E. Moln?r, I. Prok, J. Szirmai all simplicial 3-tilings have been classified, where a symmetry group acts transitively on the simplex tiles. The involved spaces depends on some rotational order parameters. When a vertex of a such simplex lies out of the absolute, e.g. in hyperbolic space H3, then truncation with its polar plane gives a truncated simplex or simply, trunc-simplex. Looking for symmetries of these tilings by simplex or trunc-simplex domains, with their side face pairings, it is possible to find all their group extensions, especia
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Winter, Martin. "Classification of Vertex-Transitive Zonotopes." Discrete & Computational Geometry, May 10, 2021. http://dx.doi.org/10.1007/s00454-021-00303-6.

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AbstractWe give a full classification of vertex-transitive zonotopes. We prove that a vertex-transitive zonotope is a $$\Gamma $$ Γ -permutahedron for some finite reflection group $$\Gamma \subset {{\,\mathrm{O}\,}}(\mathbb {R}^d)$$ Γ ⊂ O ( R d ) . The same holds true for zonotopes in which all vertices are on a common sphere, and all edges are of the same length. The classification of these then follows from the classification of finite reflection groups. We prove that root systems can be characterized as those centrally symmetric sets of vectors, for which all intersections with half-spaces,
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Chen, Jing, and Binzhou Xia. "On Isomorphisms of Vertex-transitive Graphs." Electronic Journal of Combinatorics 23, no. 2 (2016). http://dx.doi.org/10.37236/5651.

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The isomorphism problem of Cayley graphs has been well studied in the literature, such as characterizations of CI (DCI)-graphs and CI (DCI)-groups. In this paper, we generalize these to vertex-transitive graphs and establish parallel results. Some interesting vertex-transitive graphs are given, including a first example of connected symmetric non-Cayley non-GI-graph. Also, we initiate the study for GI and DGI-groups, defined analogously to the concept of CI and DCI-groups.
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Dissertations / Theses on the topic "Symmetries of vertex-transitive"

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Fadhal, Emad Alden Sir Alkhatim Abraham. "Strong simplicity of groups and vertex - transitive graphs." Thesis, University of the Western Cape, 2010. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_6774_1362393687.

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<p>In the course of exploring various symmetries of vertex-transitive graphs, we introduce the concept of quasi-normal subgroups in groups. This is done since the symmetries of vertex-transitive graphs are intimately linked to those, fait accompli, of groups. With this, we ask if the concept of strongly simple groups has a place for consideration. We have shown that for n &gt<br>5, An, the alternating group on n odd elements, is not strongly simple.</p>
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Winter, Martin. "Spectral Realizations of Symmetric Graphs, Spectral Polytopes and Edge-Transitivity." 2021. https://monarch.qucosa.de/id/qucosa%3A75215.

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A spectral graph realization is an embedding of a finite simple graph into Euclidean space that is constructed from the eigenvalues and eigenvectors of the graph's adjacency matrix. It has previously been observed that some polytopes can be reconstructed from their edge-graphs by taking the convex hull of a spectral realization of this edge-graph. These polytopes, which we shall call spectral polytopes, have remarkable rigidity and symmetry properties and are a source for many open questions. In this thesis we aim to further the understanding of this phenomenon by exploring the geometric and
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