Adjacent-Vertex-Distinguishing Total Chromatic Number of C_n×K_n

Let G be a simple graph.A k-proper total coloring of G is called adjacent-distinguishing if for arbitrary two adjacent vertices u and v,C(u)≠C(v),where C(u) is the set of the colors of u and edges which is adjacent to u.The minimum k such that G(V,E) has a k-adjacent-vertex-distinguishing total coloring is called the adjacent-vertex-distinguishing total chromatic number.The adjacent-vertex-distinguishing total chromatic number on the Cartesion product of circle Cm and complete graph Kn(Cn×Kn)is obtained..