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Enhanced power graphs of groups are weakly perfect

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Cameron_2022_Enhanced_power_graphs_AJC_v85_p100_CCBY.pdf (79.39Kb)
Date
01/02/2023
Author
Cameron, Peter J.
Phan, Veronica
Keywords
Enhanced power graph
Weakly perfect graph
Finite group
QA Mathematics
Mathematics(all)
T-NDAS
NCAD
MCC
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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.
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
2202-3518
Type
Journal article
Rights
Copyright © The author(s). Released under the CC BY 4.0 International License.
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  • University of St Andrews Research
URL
https://ajc.maths.uq.edu.au/?page=get_volumes&volume=85
https://arxiv.org/abs/2207.07156
URI
http://hdl.handle.net/10023/26528

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