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