The non-normal subgroup graph of some dihedral groups

Abstract

Let be a finite groupand is a subgroup of. The subgroup graph of in is defined as a directed simple graph with vertex set and two distinct elements and are adjacent if and only if ∈. In this paper, the work on subgroup graph is extended by defining a new graph called the non-normal subgroup graph. The subgroup graph is determined for some dihedral groupsof order 2 when the subgroup is non-normal.