Between the enhanced power graph and the commuting graph
MetadataShow full item record
Altmetrics Handle Statistics
Altmetrics DOI Statistics
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.
Cameron , P J & Kuzma , B 2022 , ' Between the enhanced power graph and the commuting graph ' , Journal of Graph Theory , vol. Early View . https://doi.org/10.1002/jgt.22871
Journal of Graph Theory
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.
DescriptionFunding: 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).
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.