Automorphism group of quasi-abelian semi-Cayley graphs

Let g be a group and r, l,s be subsets of g such that r = r^−1, l = l^−1 and 1 ∉ r ∪ l. the undirected graph (g;r, l,s) with vertex set union of g1 = {g1 | g ∈ g} and g2 = {g2 | g ∈ g}, and edge set the union of {{g1, (gr)1} | g ∈ g, r ∈ r}, {{g_2, (gl)_2} | g ∈ g, l ∈ l} and {{g_1, (gs)_2} | g ∈ g, s ∈ s} is called semi-cayley graph over g. we say that (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.