无限路的四类积图的邻和可区别全染色

Neighbor Sum Distinguishing Total Colorings of Infinite Path of Four Types of Product Graphs

图G的一个[k]-邻和可区别全染色是图G的一个[k]-全染色,其中f(v)表示点v以及所有和v相关联的边的颜色之和,满足对G的每一条边uv,都有f(u)≠f(v)成立.文章研究了无限路的四类积图的邻和可区别全染色,如无限路的笛卡尔积、直积、半强积与强积等,并得到了它们的邻和可区别全色数.

A total[k]-neighbor sum distinguishing-coloring of is a total[k]-coloring of G,let f[v]denote the sum of the color of a vertex and the colors of all incident edges of,such that for each edge uv∈E(G),f(u)≠f(v).The neighbor sum distinguishing total coloring of the four types of product graphs are studied,such as Cartesian product,direct product and semistrong product of infinite paths.The neighbor sum distinguishing total chromatic number of these product graphs are obtained.