Studying the A4-Graphs for elements of order 3 in tits group T and Mathieu group M20

Document Type : Research Paper


1 Middle Technical University, Technical Instructors Training Institute, Iraq

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


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\neq 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.