The divisibility graph $\mathscr{D}(G)$ 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 the number of connected components of $\mathscr{D}(G)$ where $G$ is a simple Zassenhaus group or an sporadic simple group.

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