Enhanced power graphs of groups are weakly perfect
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.
Citation
Cameron , P J & Phan , V 2023 , ' Enhanced power graphs of groups are weakly perfect ' , Australasian Journal of Combinatorics , vol. 85 , no. 1 , pp. 100-105 .
Publication
Australasian Journal of Combinatorics
Status
Peer reviewed
ISSN
2202-3518Type
Journal article
Rights
Copyright © The author(s). Released under the CC BY 4.0 International License.
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