# Cycles and Bipartite Graph on Conjugacy Class of Groups

### Bijan Taeri

Isfahan University of Technology, Iran

## Abstract

Let *G* be a finite non abelian group and *B(G)* be the bipartite divisor graph of a finite group related to the conjugacy classes of *G*.We prove that *B(G)* is a cycle if and only if *B(G)* is a cycle of length 6 and *G* ≅ *A* × *SL2(q)*,where *A* is abelian, and *q* ∈ {4,8}.We also prove that if *G*/*Z(G)* is simple, where *Z(G)* is the center of *G*, then *B(G)*has no cycle of length 4 if and only if *G* ≅ *A* × *SL2(q)*,where *q* ∈ {4,8}.

## Cite this article

Bijan Taeri, Cycles and Bipartite Graph on Conjugacy Class of Groups. Rend. Sem. Mat. Univ. Padova 123 (2010), pp. 233–247

DOI 10.4171/RSMUP/123-12