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On the connectivity and independence number of power graphs of groups
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dc.contributor.author | Cameron, Peter J. | |
dc.contributor.author | Jafari, Sayyed | |
dc.date.accessioned | 2020-04-01T10:30:02Z | |
dc.date.available | 2020-04-01T10:30:02Z | |
dc.date.issued | 2020-05 | |
dc.identifier.citation | Cameron , P J & Jafari , S 2020 , ' On the connectivity and independence number of power graphs of groups ' , Graphs and Combinatorics , vol. 36 , pp. 895–904 . https://doi.org/10.1007/s00373-020-02162-z | en |
dc.identifier.issn | 0911-0119 | |
dc.identifier.other | PURE: 266979039 | |
dc.identifier.other | PURE UUID: bee7e7a8-700f-4efd-a54a-fdf4b05155de | |
dc.identifier.other | ORCID: /0000-0003-3130-9505/work/71559946 | |
dc.identifier.other | Scopus: 85083113798 | |
dc.identifier.other | WOS: 000522695700001 | |
dc.identifier.uri | https://hdl.handle.net/10023/19738 | |
dc.description | Funding: EPSRC grant no EP/R014604/1. | en |
dc.description.abstract | Let G be a group. The power graph of G is a graph with vertex set G in which two distinct elements x,y are adjacent if one of them is a power of the other. We characterize all groups whose power graphs have finite independence number, show that they have clique cover number equal to their independence number, and calculate this number. The proper power graph is the induced subgraph of the power graph on the set G-{1}. A group whose proper power graph is connected must be either a torsion group or a torsion-free group; we give characterizations of some groups whose proper power graphs are connected. | |
dc.format.extent | 10 | |
dc.language.iso | eng | |
dc.relation.ispartof | Graphs and Combinatorics | en |
dc.rights | Copyright © The Author(s) 2020. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ | en |
dc.subject | Power graph | en |
dc.subject | Connectivity | en |
dc.subject | Independence number | en |
dc.subject | Cyclic | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | On the connectivity and independence number of power graphs of groups | en |
dc.type | Journal article | en |
dc.description.version | Publisher PDF | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | https://doi.org/10.1007/s00373-020-02162-z | |
dc.description.status | Peer reviewed | en |
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