On the isomorphisms of Cayley graphs of Abelian groups

  • Authors:
  • Yan-Quan Feng;Yan-Pei Liu;Ming-Yao Xu

  • Affiliations:
  • Department of Mathematics, Northern Jiaotong University, Beijing 100044, People's Republic of China;Department of Mathematics, Northern Jiaotong University, Beijing 100044, People's Republic of China;Department of Mathematics, Peking University, Beijing 100871, People's Republic of China

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2002

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Abstract

Let G be a finite group, S a subset of G\{1}, and let Cay (G, S) denote the Cayley digraph of G with respect to S. If, for any subset T of G\{1}, Cay(G, S) ≅ Cay(G, T) implies that Sα = T for some α ∈ Aut(G), then S is called a CI-subset. The group G is called a CIM-group if for any minimal generating subset S of G, S ∪ S-1 is a CI-subset. In this paper, CIM-abelian groups are characterized.