Characterization of finite groups by their commuting graph

Iranmanesh, A. and Jafarzadeh, A. (2007) Characterization of finite groups by their commuting graph. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 23 (1). pp. 7-13. ISSN 0866-0174

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Abstract

The commuting graph of a group G, denoted by Γ(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 Γ(G) ∼= Γ(M), then G ∼= M. In this paper we prove this conjecture for many simple groups.

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