Matching in power graphs of finite groups
Abstract
The power graph P(G) of a finite group G is the undirected simple graph with vertex set G, where two elements are adjacent if one is a power of the other. In this paper, the matching numbers of power graphs of finite groups are investigated. We give upper and lower bounds, and conditions for the power graph of a group to possess a perfect matching. We give a formula for the matching number for any finite nilpotent group. In addition, using some elementary number theory, we show that the matching number of the enhanced power graph Pe(G) of G (in which two elements are adjacent if both are powers of a common element) is equal to that of the power graph of G.
Citation
Cameron , P J , Swathi , V V & Sunitha , M S 2022 , ' Matching in power graphs of finite groups ' , Annals of Combinatorics , vol. 26 , no. 2 , pp. 379-391 . https://doi.org/10.1007/s00026-022-00576-5
Publication
Annals of Combinatorics
Status
Peer reviewed
ISSN
0218-0006Type
Journal article
Description
Funding: The author Swathi V V acknowledges the support of Council of Scientific and Industrial Research, India (CSIR) (Grant No-09/874(0029)/2018-EMR-I), and DST, Government of India, ‘FIST’ (No.SR/FST /MS-I/2019/40).Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.