Conjugacy classes of finite groups and graph regularity

2013/06/06 by Bianchi, Mariagrazia, Camina, Rachel D., Herzog, Marcel +1 · 1 citation
#20E45 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1306.1558

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 vertices.

Cited by

• Groups with conjugacy classes of coprime sizes

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