Given a connected graph Δ, a group G can be constructed in such a way that Δ is often isomorphic to a subgraph of the commuting graph $\mathcal{KG}(\mathrm{\Delta })$ of G. We show that, with one exception, $\mathcal{KG}(\mathrm{\Delta })$ is connected, and in this latter case its diameter is at most that of Δ. If Δ is a path of length $n>2$, then $\mathrm{diam}(\mathcal{KG}(\mathrm{\Delta }))=n$.

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关于 Giudici 和 Parker 关于组通勤图的构造

给定一个连通图 Δ，可以构造一个群G ，使得 Δ 通常同构于通勤图的子图$\mathcal{公斤}(\mathrm{\Delta })$的G。我们证明，除了一个例外，$\mathcal{公斤}(\mathrm{\Delta })$是相连的，在后一种情况下，它的直径最多为 Δ。如果 Δ 是一条长度为$n>2$， 然后$\mathrm{直径}(\mathcal{公斤}(\mathrm{\Delta }))=n$.