Description of the A۴-graph for elements of order three in certain miscellaneous groups

Suppose that G is a finite group and X=\textit{t}^{G}   be a conjugacy class of an elements of order ۳, \textit{t}\in G .The A۴-graph, is a simple undirected graph stand for \textit{A}{_{۴}}(G,X), whose vertex set X and two vertices \textit{x, y}\in X are adjacent if they are different and satisfy  \textit{xy}^{-۱} = \textit{yx}^{-۱}. In this article, the orbits under the action of C_{G}(\textit{t}) on X are analyzed, along with  the description of the algebraic structure of the subgroup <\textit{t,x}>  such that \textit{x} is a C_{G}(\textit{t}) -orbit representative is provided.

کلیدواژه ها:

Finite simple groups ، A۴-graph ، connectivity ، cliques