On adjacent vertex-distinguishing total colorings of graphs P_m*P_n

Let G_1 and G_2 be finite simple graphs.The concept of graph G_1*G_2 is introduced, and adjacent vertexdistinguishing total coloring numbers of graphs P_m*P_n are given. χ_ at (P_m*P_n)=5, when m=n=2; 7, when m=2,n2 or m2,n=2; 9, when m=n=3; 10, when m≥3,n3 or m3,n≥3.