Results 1 to 10 of about 21,101 (124)
ALTERNATING AND SYMMETRIC GROUPS WITH EULERIAN GENERATING GRAPH [PDF]
Forum of Mathematics, Sigma, 2017 Given a finite group $G$ , the generating graph $\unicode[STIX]{x1D6E4}(G)$
ANDREA LUCCHINI, CLAUDE MARION
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Minimum Neighborhood of Alternating Group Graphs [PDF]
IEEE Access, 2019 The minimum neighborhood and combinatorial property are two important indicators of fault tolerance of a multiprocessor system. Given a graph G, θG(q) is the minimum number of vertices adjacent to a set of q vertices of G (1 ≤ q ≤ |V(
Yanze Huang +3 more
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Metric properties of Cayley graphs of alternating groups
Karpatsʹkì Matematičnì Publìkacìï, 2021 A well known diameter search problem for finite groups with respect to its systems of generators is considered. The problem can be formulated as follows: find the diameter of a group over its system of generators.
M.S. Olshevskyi
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Characterization of some alternating groups by order and largest element order [PDF]
AUT Journal of Mathematics and Computing, 2022 The prime graph (or Gruenberg-Kegel graph) of a finite group is a well-known graph. In this paper, first, we investigate the structure of the finite groups with a non-complete prime graph.
Ali Mahmoudifar, Ayoub Gharibkhajeh
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Examples and Counterexamples, 2023 A new strongly regular graph with parameters (81,30,9,12) is found as a graph invariant under certain subgroup of the full automorphism group of the previously known strongly regular graph discovered in 1981 by J. H. van Lint and A. Schrijver.
Dean Crnković, Andrea Švob
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McKay graphs for alternating and classical groups [PDF]
Transactions of the American Mathematical Society, 2021 Let $G$ be a finite group, and $ $ a nontrivial character of $G$. The McKay graph $\mathcal{M}(G, )$ has the irreducible characters of $G$ as vertices, with an edge from $ _1$ to $ _2$ if $ _2$ is a constituent of $ _1$. We study the diameters of McKay graphs for finite simple groups $G$.
Martin W. Liebeck +2 more
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Divisibility Graph for Symmetric and Alternating Groups [PDF]
Communications in Algebra, 2015 Let $X$ be a non-empty set of positive integers and $X^*=X\setminus \{1\}$. The divisibility graph $D(X)$ has $X^*$ as the vertex set and there is an edge connecting $a$ and $b$ with $a, b\in X^*$ whenever $a$ divides $b$ or $b$ divides $a$. Let $X=cs~{G}$ be the set of conjugacy class sizes of a group $G$. In this case, we denote $D(cs~{G})$ by $D(G)$.
Abdolghafourian, Adeleh +1 more
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Automorphism group of the complete alternating group graph [PDF]
Applied Mathematics and Computation, 2017 9 pages, 1 ...
Huang, Xueyi, Huang, Qiongxiang
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A 2-arc Transitive Hexavalent Nonnormal Cayley Graph on A119
Mathematics, 2021 A Cayley graph Γ=Cay(G,S) is said to be normal if the base group G is normal in AutΓ. The concept of the normality of Cayley graphs was first proposed by M.Y.
Bo Ling, Wanting Li, Bengong Lou
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2-Arc-transitive Cayley graphs on alternating groups
Journal of Algebra, 2022 An interesting fact is that most of the known connected $2$-arc-transitive nonnormal Cayley graphs of small valency on finite simple groups are $(\mathrm{A}_{n+1},2)$-arc-transitive Cayley graphs on $\mathrm{A}_n$. This motivates the study of $2$-arc-transitive Cayley graphs on $\mathrm{A}_n$ for arbitrary valency.
Jiangmin Pan, Binzhou Xia, Fugang Yin
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