Conjugacy classes of finite groups and graph regularity

Mariagrazia Bianchi, Rachel D. Camina, Marcel Herzog, Emanuele Pacifici

Research output: Contribution to journalArticlepeer-review

Abstract

Given a finite group G, denote by Γ(G) the simple undirected graph whose vertices are the distinct sizes of noncentral conjugacy classes of G, and set two vertices of Γ(G) to be adjacent if and only if they are not coprime numbers. In this note we prove that, if Γ(G) is a k-regular graph with k ≥ 1, then Γ(G) is a complete graph with k+1$k+1$ vertices.

Original languageEnglish
Pages (from-to)3167-3172
Number of pages6
JournalForum Mathematicum
Volume27
Issue number6
DOIs
StatePublished - 1 Nov 2015

Keywords

  • Finite groups
  • conjugacy class sizes

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