Further Results on Intersection Power Graph of Finite Groups

Abstract

Let G be a finite group with identity element e. The intersection power graph ΓIP (G) of G is the undirected graph whose vertex set is the elements of G and two distinct vertices a, b are adjacent in ΓIP (G) if there exists a non-identity element c such that a p = c = b q for two positive integers p, q and e is adjacent to all other vertices of ΓIP (G). In the present paper, we determine some finite groups whose intersection power graphs having book thickness at most two. Also, we attain a lower bound for α0(ΓIP (G)).