Enhanced power graphs of groups are weakly perfect
Combinatorics
2022-07-18 v1 Group Theory
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 is weakly perfect: its clique number and chromatic number are equal to the maximum order of an element of . The proof requires a combinatorial lemma. We give some remarks about related graphs.
Cite
@article{arxiv.2207.07156,
title = {Enhanced power graphs of groups are weakly perfect},
author = {Peter J. Cameron and Veronica Phan},
journal= {arXiv preprint arXiv:2207.07156},
year = {2022}
}