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On the connectivity and independence number of power graphs of groups

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Cameron_Jafari2020_Article_OnTheConnectivityAndIndependen.pdf (242.8Kb)
Date
05/2020
Author
Cameron, Peter J.
Jafari, Sayyed
Keywords
Power graph
Connectivity
Independence number
Cyclic
QA Mathematics
T-NDAS
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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.
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
Publication
Graphs and Combinatorics
Status
Peer reviewed
DOI
https://doi.org/10.1007/s00373-020-02162-z
ISSN
0911-0119
Type
Journal article
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/
Description
Funding: EPSRC grant no EP/R014604/1.
Collections
  • University of St Andrews Research
URI
http://hdl.handle.net/10023/19738

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