Isomorphisms of generalized Cayley graphs
نویسندگان
چکیده
منابع مشابه
Isomorphisms of Cayley graphs on nilpotent groups
Let S be a finite generating set of a torsion-free, nilpotent group G. We show that every automorphism of the Cayley graph Cay(G;S) is affine. (That is, every automorphism of the graph is obtained by composing a group automorphism with multiplication by an element of the group.) More generally, we show that if Cay(G1;S1) and Cay(G2;S2) are connected Cayley graphs of finite valency on two nilpot...
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A Cayley graph Cay(G, S) of a group G is called a CI-graph if whenever T is another subset of G for which Cay(G, S) ∼= Cay(G, T ), there exists an automorphism σ of G such that Sσ = T . For a positive integer m, the group G is said to have the m-CI property if all Cayley graphs of G of valency m are CI-graphs; further, if G has the k-CI property for all k ≤ m, then G is called an m-CI-group, an...
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Let $Gamma$ be a graph with adjacency eigenvalues $lambda_1leqlambda_2leqldotsleqlambda_n$. Then the energy of $Gamma$, a concept defined in 1978 by Gutman, is defined as $mathcal{E}(G)=sum_{i=1}^n|lambda_i|$. Also the Estrada index of $Gamma$, which is defined in 2000 by Ernesto Estrada, is defined as $EE(Gamma)=sum_{i=1}^ne^{lambda_i}$. In this paper, we compute the eigen...
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متن کاملGeneralized Cayley Graphs of Rectangular Groups
We describe generalized Cayley graphs of rectangular groups, so that we obtain (1) an equivalent condition for two Cayley graphs of a rectangular group to be isomorphic to each other, (2) a necessary and sufficient condition for a generalized Cayley graph of a rectangular group to be (strong) connected, (3) a necessary and sufficient condition for the colour-preserving automorphism group of suc...
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ژورنال
عنوان ژورنال: Ars Mathematica Contemporanea
سال: 2018
ISSN: 1855-3974,1855-3966
DOI: 10.26493/1855-3974.1345.ae6