some results on the complement of the intersection graph of subgroups of a finite group

In this article we consider groups g such that g admits at least one nontrivial subgroup (recall that a subgroup h of g is said to be nontrivial if h /∈ {g, {e}}). let g be a group. recall that the intersection graph of subgroups of g, denoted by γ(g), is an undirected graph whose vertex set is the set of all nontrivial subgroups of g and distinct vertices h, k are joined by an edge in this graph if and only if h ∩ k ̸= {e}. let g be a finite group. the aim of this article is to investigate the interplay between the group-theoretic properties of a finite group g and the graph-theoretic properties of the complement of γ(g).