Abstract: Let A be a set consisted of all combinations which are made up of four numbers selected from the set {1,2,…,n} discretionarily.By the triangle compositor,the author obtain that for any two adjacent elements C and D in set A,they contain the same three elements.In this paper,using the above idea and n+8k3-n3≡0 (mod 4),it is proved that when n=11+8k(k=0,1,…) and n-14/2+2 <m≤n4/2+2,vertex distinguishing total chromatic number of product Pm×P3 is n.

Key words: product graph, vertex distinguishing toal coloring, vertex distinguishing total chromatic number, triangle sequence