On the Isomorphisms of Cayley Graphs of Abelian Groups

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.