The intersection subgroup graph of a group

Abstract

Let G be a group. In this paper, we introduce and study the intersection subgroup graph of G as the (simple) graph with vertices the nontrivial subgroups H of G such that for some nontrivial subgroup K of G, and distinct vertices H and K are adjacent if and only if . We investigate when is a nonempty, finite, complete, complete bipartite, or planar graph.