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Between the enhanced power graph and the commuting graph

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Cameron_2022_Between_the_enhanced_power_graph_JGraphTheory_22871_CC.pdf (393.3Kb)
Date
02/2023
Author
Cameron, Peter J.
Kuzma, Bojan
Keywords
Commuting graph
Enhanced power graph
Central extension
Schur multiplier
Bogomolov multiplier
QA Mathematics
Mathematics(all)
T-NDAS
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Abstract
The purpose of this note is to define a graph whose vertex set is a finite group G, whose edge set is contained in that of the commuting graph of G and contains the enhanced power graph of G. We call this graph the deep commuting graph of G. Two elements of G are joined in the deep commuting graph if and only if their inverse images in every central extension of G commute. We give conditions for the graph to be equal to either of the enhanced power graph and the commuting graph, and show that automorphisms of G act as automorphisms of the deep commuting graph.
Citation
Cameron , P J & Kuzma , B 2023 , ' Between the enhanced power graph and the commuting graph ' , Journal of Graph Theory , vol. 102 , no. 2 , pp. 295-303 . https://doi.org/10.1002/jgt.22871
Publication
Journal of Graph Theory
Status
Peer reviewed
DOI
https://doi.org/10.1002/jgt.22871
ISSN
0364-9024
Type
Journal article
Rights
Copyright © 2022 The Authors. Journal of Graph Theory published by Wiley Periodicals LLC. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
Description
Funding: The second author acknowledges the financial support from the Slovenian Research Agency, ARRS (research core funding No. P1-0222, No. P1-0285, and research project No. N1-0210).
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/25793

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