On the regularity of a graph related to conjugacy classes of groups

被引：8

作者：

Bianchi, Mariagrazia ^{[1
]}

Herzog, Marcel ^{[2
]}

Pacifici, Emanuele ^{[1
]}

Saffirio, Giulio ^{[1
]}

机构：

[1] Univ Milan, Dipartimento Matemat F Enriques, I-20133 Milan, Italy

[2] Tel Aviv Univ, Raymond & Beverly Sackler Fac Exact Sci, Sch Math Sci, IL-69978 Tel Aviv, Israel

来源：

EUROPEAN JOURNAL OF COMBINATORICS | 2012年 / 33卷 / 07期

关键词：

D O I：

10.1016/j.ejc.2012.03.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a finite group G, denote by Gamma (G) the simple undirected graph whose vertices are the (distinct) non-central conjugacy class sizes of G, and for which two vertices of Gamma (G) are adjacent if and only if they are not coprime numbers. In this note we prove that Gamma (G) is a 2-regular graph if and only if it is a complete graph with three vertices, and Gamma (G) is a 3-regular graph if and only if it is a complete graph with four vertices. (c) 2012 Elsevier Ltd. All rights reserved.

引用

页码：1402 / 1407

页数：6

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