Structure of intersection graphs

Abstract

Let G be a finite group and let N be a fixed normal subgroup of G. In this paper, a new kind of graph on G, namely the intersection graph is defined and studied. We use to denote this graph, with its vertices are all normal subgroups of G and two distinct vertices are adjacent if their intersection in N. We show some properties of this graph. For instance, the intersection graph is a simple connected with diameter at most two. Furthermore we give the graph structure of for some finite groups such as the symmetric, dihedral, special linear group, quaternion and cyclic groups.

Keywords

• connected graph, normal subgroup, diameter