Document Type : Research Paper

Authors

• Zainab Hasan Msheree ¹
• Mohammed Mukheef Abed ¹
• Wissam Fadhel Abid ²

¹ Middle Technical University, Technical Instructors Training Institute, Iraq

² Middle Technical University, Institute of Technology, Baghdad, Iraq

Abstract

Assume that $X$ is a subset of the finite group $G$. The A4-graph is known as a simple graph denoted by ${\mathcal{A}}_4(G,X)$ having $X$ as a vertex set and two vertices $x,y\in X,$ is linked by an edges if $x\ne y$ and ${xy}^{-1}={yx}^{-1}$. In this paper, we consider ${\mathcal{A}}_4(G,X)$ when $G$ is either Tits group T or Mathieu group $M_{20}$ and $X$ is $G$-conjugacy class of elements of order three. Valuable results reached, for example, disc structure, girth, clique number, and diameters of the A4-graph.

Keywords

• Finite simple groups
• A4-graph
• connectivity
• cliques