The complement of subgroup graph of a group

Let g be a finite group and h a subgroup of g. in 2012,david f. anderson et al. introduced the subgroup graph of h in g as a simple graph with vertex set consisting all elements of g and two distinct vertices x and y are adjacent if and only if xy ε h. they denoted this graph by γh(g). in this paper,we consider the complement of γh(g),denoted by γh(g) and will give some graph properties of this graph,for instance diameter,girth,independent and dominating sets,regularity. moreover,the structure of this graph,planerity and 1-planerity are also investigated in the paper.