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

Sucharita Biswas, Peter J. Cameron, Angsuman Das*, Hiranya Kishore Dey

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The 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.
Original languageEnglish
Article number105932
Number of pages31
JournalJournal of Combinatorial Theory, Series A
Volume208
Early online date21 Jun 2024
DOIs
Publication statusE-pub ahead of print - 21 Jun 2024

Keywords

  • Power graph
  • Enhanced power graph
  • Twin reduction
  • Gruenberg-Kegel graph (prime graph)

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