关于C_m·C_n,C_m·S_n和C_m·K_n的邻点可区别全色数

On the Adjacent Vertex Distinguishing Total Chromatic Number of C_m·C_n,C_m·S_n and C_m·K_n

一个图的正常全染色如果相邻点的点染色及其关联边染色集合是不同的,则称为图的邻点可区别全染色,其所用到的最少颜色数称为图的邻点可区别全色数.该文得到了冠图圈与圈(星,完全图)的邻点可区别全色数.

Let G be a simple graph.Let f be a mapping from V(G)∪E(G) to {1,2,…,k}.Let Cf(v)={f(v)}∪{f(ωv)|ω∈V(G),ωv∈E(G)} for every v∈V(G).If f is a k-proper-total-coloring,and if Cf(u)≠Cf(v) for uv∈E(G),then f is called k-adjacent-vertex-distinguishing total coloring of G(k-AVDTC) of G forshort).Let χat(G)=min{k|G has a k-adjacent-vertex-distinguishing-total-coloring}.Then χat(G) is called the adjacent-vertex-distinguishing total chromatic number.In this paper,we have obtained the adjacent-vertex-distinguishing total chromatic number of Cm·Cn,Cm·Sn and Cm·Kn.