Analysing the Result Involution Graph of the Group J3

Abstract

Assume that G be a finite group and let I(G) be the set of the involution elements in G. The result involution graph denoted by , , is an undirected simple graph having the elements of G as a vertex set. Moreover, two vertices in are connected by an edge if they are distinct and their product belong to I(G). The objective of this work is to investigate the result involution graph for the Janko group J3. In this paper we compute different result involution graph features, such as the radius, the diameter, the clique number, and the girth. Furthermore, the connectedness of the result involution graph is determined. All of the steps needed for analyzing the result involution graph were carried out using the computational technique along with theoretical support.

Keywords

• Janko Groups, Result Involution Graph, Connectedness, Girth