Structure And Vertex Transitive Property Of Directed Cayley Graphs On Completely Simple Semigroup With Degree 2

In this paper, we studied the structure and vertex transitive property of directed Cayley graphs Cayley(S, A) on completely simple semigroup with degree 2 ,First ,we get the structurethat Cayley(S, A)≌ID(n, j,k)∪M,where ID(n, j,k) is directed I graph, M = {(v_i,u_i+h) i = 0,1…n -1} is perfect matching of Cayley(S, A) .Moreover, if b≠j + k we discuss vertex transitivity and property of Cayley(S, A) ,and we discuss the structure and vertex transitivity of ID(n, j, k)∪M under two cases of b = j + k + t and b = j + k-t if b = j + k-t and t = j we get the sufficient and necessary condition that when ID(n, j, k)∪M is vertex transitive .Furthermore ,if b≠j + k an b = 0(modn)we get the sufficient and necessary condition that when ID(n, j,k)∪Mis vertex transitive .At last we applied it to the directed Cayley graphs on completely simple semigroup with degree 2 and obtain some results as structure and vertex transitive.