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dc.contributor.authorCameron, Peter J.
dc.contributor.authorKuzma, Bojan
dc.identifier.citationCameron , P J & Kuzma , B 2022 , ' Between the enhanced power graph and the commuting graph ' , Journal of Graph Theory , vol. Early View .
dc.identifier.otherPURE: 280548389
dc.identifier.otherPURE UUID: a29c8009-b3bf-49b1-9fa8-d1e66f9dbdef
dc.identifier.otherORCID: /0000-0003-3130-9505/work/117211019
dc.identifier.otherWOS: 000837178300001
dc.identifier.otherScopus: 85136820241
dc.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).en
dc.description.abstractThe 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.
dc.relation.ispartofJournal of Graph Theoryen
dc.rightsCopyright © 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.en
dc.subjectCommuting graphen
dc.subjectEnhanced power graphen
dc.subjectCentral extensionen
dc.subjectSchur multiplieren
dc.subjectBogomolov multiplieren
dc.subjectQA Mathematicsen
dc.titleBetween the enhanced power graph and the commuting graphen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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