Subgroup intersection graph of finite abelian groups

Let G be a finite group with identity e. The subgroup intersection graph Gamma_SI (G) of G isa graph with vertex set G e and two distinct vertices x and y are adjacent if and only if | i ∩ | | > 1. In this paper, we obtain a lower bound for the independence number of subgroup intersection graph. We characterize certain classes of subgroup intersection graphs corresponding to finite abelian groups. Finally, wecharacterize groups whose automorphism group is the same as that of its subgroup intersection graph.