**
Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 23, No. 1, pp. 7-13 (2007)
**

#
Characterization of finite groups by their commuting graph

##
A. Iranmanesh and A. Jafarzadeh

Tarbiat Modares University, Tehran

**Abstract:** The commuting graph of a group $G$, denoted by $\G(G)$, is a simple graph whose vertices are all non-central elements of $G$ and two distinct vertices $x,y$ are adjacent if $xy=yx$. In [1] it is conjectured that if $M$ is a simple group and $G$ is a group satisfying $\G(G)\cong\G(M)$, then $G\cong M$. In this paper we prove this conjecture for many simple groups.

**Keywords:** Simple group, Commuting graph, prime graph, order components

**Classification (MSC2000):** 20D05; 20D06, 05C25

**Full text of the article:**

[Previous Article] [Next Article] [Contents of this Number]

*
© 2007 ELibM and
FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition
*