图G的一个k-全着色满足G的任何路长为2的点,边着色均不相同,我们称它为G的k-星全着色.图G的全部k-星全着色中最小的k称为图G的星全色数,记为χst(G).讨论一些圈的星全染色问题,得到了图D(Cn)(n=0(mod 3)和n=0(mod 5)),Cn^2(n=0(mod 20)和n=0(mod 28))以及Cn^3(n=0(mod 28)和n=0(mod 36))的星全色数.
A proper total k-coloring of a graph G is a star total k-coloring if the colorings of vertices and edges of any path of length 3 in G are all different. The least number of k spanning over all star total k-colorings of G, denoted by Хst,(G), is called the star total chromatic number of G. In this paper, we searched the star total chromatic numbers on some graphs and obtained the star total chromatic numbers of D(Cn)(n : 0(mod 3)and n = 0(mod 5)),Cn^2(n = 0(mod 20) and n= 0(mod 28)),Cn^3(n = 0(mod 28)and n : 0(mod 36)).