English

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 GG is weakly perfect: its clique number and chromatic number are equal to the maximum order of an element of GG. The proof requires a combinatorial lemma. We give some remarks about related graphs.

Keywords

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}
}
R2 v1 2026-06-25T00:55:42.792Z