Between the enhanced power graph and the commuting graph
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
ISSN
0364-9024Type
Journal article
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).Collections
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