Finite groups with graphs containing no triangles

Abstract

Let G be a non-Abelian finite group, Γ( G) the attached graph related to its conjugacy classes. The aim of this paper is to prove that the symmetric group S 3, the dihedral group D 5, the three pairwise non-isomorphic non-Abelian groups of order 12, and the non-Abelian group T 21 of order 21, is the complete list of all G such that Γ( G) contains no triangles.