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main supergraph; Suzuki group
Let $G$ be a finite group. The main supergraph $\mathcal{S}(G)$ is a graph with vertex set $G$ in which two vertices $x$ and $y$ are adjacent if and only if $o(x) \mid o(y)$ or $o(y)\mid o(x)$. In this paper, we will show that $G\cong Sz(q)$ if and only if $\mathcal{S}(G)\cong \mathcal{S}(Sz(q))$, where $q=2^{2m+1}\ge 8$.
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