关于图P_m*P_n的邻点可区别全染色

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

设G1,G2是有限简单图,引入了图G1*G2的概念,给出了图Pm*Pn(n≥2,m≥2)的邻点可区别全色数χat(Pm*Pn)=5,当m=n=2时;7,当m=2,n>2或m>2,n=2时;9,当m=n=3时;10,当m≥3,n>3或m>3,n≥3时.

Let G1 and G2 be finite simple graphs. The concept of graph G1＊ G2 is introduced, and adjacent vertex-distinguishing total coloring numbers of graphs Pm＊Pn are given,χα1（Pm＊Pn）={5,when m=n=2;7,when m=2,n〉2 or m〉2,n=2;9,when m=n=3;10,when m≥3,n〉3 or m〉3,n≥3.