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On the difference of the enhanced power graph and the power graph of a finite group

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dc.contributor.authorBiswas, Sucharita
dc.contributor.authorCameron, Peter J.
dc.contributor.authorDas, Angsuman
dc.contributor.authorDey, Hiranya Kishore
dc.date.accessioned2024-07-11T14:30:02Z
dc.date.available2024-07-11T14:30:02Z
dc.date.issued2024-11
dc.identifier303585366
dc.identifier15c76b4e-8f88-4f8b-8793-d8a46b9e8c45
dc.identifier.citationBiswas , S , Cameron , P J , Das , A & Dey , H K 2024 , ' On the difference of the enhanced power graph and the power graph of a finite group ' , Journal of Combinatorial Theory, Series A , vol. 208 , 105932 . https://doi.org/10.1016/j.jcta.2024.105932en
dc.identifier.issn0097-3165
dc.identifier.otherORCID: /0000-0003-3130-9505/work/162167821
dc.identifier.urihttps://hdl.handle.net/10023/30150
dc.descriptionFunding: The first author is supported by the PhD fellowship of CSIR (File no. 08/155 (0086)/2020 − EMR − I), Govt. of India. The second author acknowledges the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Groups, representations and applications: new perspectives (supported by EPSRC grant no. EP/R014604/1), where he held a Simons Fellowship. The third author acknowledges the funding of DST grant SR/F ST/MS − I/2019/41 and MT R/2022/000020, Govt. of India. The fourth author acknowledges SERB-National Post-Doctoral Fellowship (File No. PDF/2021/001899) during the preparation of this work.en
dc.description.abstractThe difference graph of a finite group D (G) is the difference of the enhanced power graph of G and the power graph of G, where all isolated vertices are removed. In this paper we study the connectedness and perfectness of D (G) with respect to various properties of the underlying group G. We also find several connections between the difference graph of G and the Gruenberg-Kegel graph of G. We also examine the operation of twin reduction on graphs, a technique which produces smaller graphs which may be easier to analyze. Applying this technique to simple groups can have a number of outcomes, not fully understood, but including some graphs with large girth.
dc.format.extent31
dc.format.extent412559
dc.language.isoeng
dc.relation.ispartofJournal of Combinatorial Theory, Series Aen
dc.subjectPower graphen
dc.subjectEnhanced power graphen
dc.subjectTwin reductionen
dc.subjectGruenberg-Kegel graph (prime graph)en
dc.subjectQ Scienceen
dc.subjectMathematics(all)en
dc.subjectT-DASen
dc.subject.lccQen
dc.titleOn the difference of the enhanced power graph and the power graph of a finite groupen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doi10.1016/j.jcta.2024.105932
dc.description.statusPeer revieweden


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