S_m×S_n,S_m×F_n和S_m×W_n的点可区别全色数

Vertex-distinguishing Total Chromatic Nnumber of S_m×S_n,S_m×F_n and S_m×W_n

图的一个正常的全染色如果满足不同点的邻点及其关联边的色集合不同,则称该染色法为点可区别全染色,其所用最少颜色数称为该图的点可区别全色数.给出了星和星、星和扇、星和轮的笛卡尔积图的点可区别全色数.

A proper total-coloring is called vertex-distinguishing the color-sets of incident vertices and incident edges for different vertices are different. The minimum number of colors of a vertex-distinguishing total-coloring is called the vertex-distinguishing total chromatic number of the graph. In this paper,the vertex-distinguishing total chromatic number of Sm×Sn,Sm×Fn and Sm×Wn are given.