The isomorphism of generalized Cayley graphs on finite non-abelian simple groups

Abstract

The isomorphism problem is a fundamental problem for algebraic and combinatorial structures, particularly in relation to Cayley graphs. Let Xi=GC(G,Si,αi),(i=1,2) be generalized Cayley graphs. If whenever X1≅X2, it implies that α2=α1γ and S2=g−1S1γgα2 for some g∈G and γ∈Aut(G), then G is a strongly generalized Cayley isomorphism (GCI)-group. In this study, we defined (strongly, restricted) m-GCI-groups. These definitions are similar to those of m-CI-groups for Cayley graphs. Our main results demonstrate that a finite non-abelian simple group G is a restricted 2-GCI-group if and only if G is one of A5, L2(8), M11, Sz(8), or M23, and G is a 2-GCI-group if and only if G is A5 or L2(8).