Majid Arezoomand - Department of Mathematics, Larestan University

Let G be a group and R,L,S be subsets of G such that R=R^{-۱}, L=L^{-۱} and ۱\notin R\cup L. The undirected graph \SC(G;R,L,S) with vertex set  union of G_۱=\{g_۱\mid g\in G\} and G_۲=\{g_۲\mid g\in G\}, and edge set the union of \{\{g_۱,(gr)_۱\}\mid g\in G, r\in R\}, \{\{g_۲,(gl)_۲\}\mid g\in G,l\in L\} and \{\{g_۱,(gs)_۲\}\mid g\in G,s\in S\} is called semi-Cayley graph over G.  We say that \SC(G;R,L,S) is quasi-abelian if R,L and S are a  union of conjugacy classes of G. In this paper, we study the automorphism group of quasi-abelian semi-Cayley graphs.

Semi-Cayley graph, quasi-abelian semi-Cayley graph, automorphism of graph