On the non-inverse graph of a group

Abstract

Let (G, * ) be a finite group and S = {u ∈ G|u = u −1 }, then the inverse graph is defined as a graph whose vertices coincide with G such that two distinct vertices u and v are adjacent if and only if either u * v ∈ S or v * u ∈ S. In this paper, we introduce a modified version of the inverse graph, called i * -graph associated with a group G. The i * -graph is a simple graph with vertex set consisting of elements of G and two vertices x, y ∈ Γ are adjacent if x and y are not inverses of each other. We study certain properties and characteristics of this graph. Some parameters of the i *graph are also determined.