Identity Intersection graph of a group

Abstract

Let G be a group with identity e. The Identity Intersection graph Γ_II(G) of G is a graph with V(Γ_II(G))=G and two distinct vertices x and y are adjacent in Γ_II(G) if and only if < x >∩ < y >= {e}, where < x >is the cyclic subgroup of G generated by x∈G. In this paper, we want to explore how the group theoretical properties of G can effect on the graph theoretical properties of Γ_II(G). Some characterizations for fundamental properties of Γ_II(G) have also been obtained.