On divisibility graph for simple Zassenhaus groups

Abstract

The divisibility graph $D(G)$ for a finite group $G$ is a graph with vertex set $cs~(G)\setminus\{1\}$ where $cs~(G)$ is the set of conjugacy class sizes of $G$. Two vertices $a$ and $b$ are adjacent whenever $a$ divides $b$ or $b$ divides $a$. In this paper we will find $D(G)$ where $G$ is a simple Zassenhaus group.