# 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 $G≃A×SL_{2}(q)$, 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 $G≃A×SL_{2}(q)$, 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