Matching in power graphs of finite groups

Peter J. Cameron*, V. V. Swathi, M. S. Sunitha

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)379-391
JournalAnnals of Combinatorics
Issue number2
Early online date13 Mar 2022
Publication statusPublished - Jun 2022


  • Group
  • Power graph
  • Matching
  • Enhanced power graph
  • Perfect matching


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