Enhanced power graphs of groups are weakly perfect

Peter J. Cameron; Veronica Phan

Enhanced power graphs of groups are weakly perfect

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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.

Original language	English
Pages (from-to)	100-105
Number of pages	6
Journal	Australasian Journal of Combinatorics
Volume	85
Issue number	1
Early online date	29 Nov 2022
Publication status	Published - 1 Feb 2023

Keywords

Enhanced power graph
Weakly perfect graph
Finite group

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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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T1 - Enhanced power graphs of groups are weakly perfect

AU - Cameron, Peter J.

AU - Phan, Veronica

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AB - 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.

KW - Enhanced power graph

KW - Weakly perfect graph

KW - Finite group

UR - https://ajc.maths.uq.edu.au/?page=get_volumes&volume=85

UR - https://arxiv.org/abs/2207.07156

M3 - Article

SN - 2202-3518

VL - 85

SP - 100

EP - 105

JO - Australasian Journal of Combinatorics

JF - Australasian Journal of Combinatorics

IS - 1

ER -

Enhanced power graphs of groups are weakly perfect

Abstract

Keywords

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