Giovanni Cutolo: papers

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36: G. Cutolo
On a construction by Giudici and Parker on commuting graphs of groups
J. Combin. Theory Ser. A, to appear.
doi: 10.1016/j.jcta.2022.105666
Abstract Full Text

Abstract

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

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