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arXiv · 2207.07156

Enhanced power graphs of groups are weakly perfect

Peter J. Cameron·Veronica Phan
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Abstract

A graph is weakly perfect if its clique number and chromatic number are equal. We show that the enhanced power graph of a finite group $G$ is weakly perfect: its clique number and chromatic number are equal to the maximum order of an element of $G$. The proof requires a combinatorial lemma. We give some remarks about related graphs.

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Peter J. Cameron, Veronica Phan. 2022-07-14. Enhanced power graphs of groups are weakly perfect. https://arxiv.org/abs/2207.07156

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