The isomorphism between two fundamental groups by Cayley graphs

Abstract

Let G1 and G2 be two finite groups and let Cay(G1, S1) and Cay(G2, S2) be the corresponding Cayley graphs of these groups, respectively. By [2] and [8], one can define the fundamental group π1 (Γ, v) by using any connected graph Γ with a fixed vertex v. In this paper we give sufficient conditions for any two fundamental groups which are obtained by Cayley graphs Cay(G1, S<inf>1</inf>) and Cay(G<inf>2</inf>, S<inf>2</inf>) to be isomorphic. At the final part of the paper, we present some examples of this result.