摘要
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.
出处
《江西师范大学学报(自然科学版)》
CAS
北大核心
2008年第4期403-407,共5页
Journal of Jiangxi Normal University(Natural Science Edition)
基金
国家自然科学基金(No.10771197)资助项目
关键词
圈
星
完全图
冠图
邻点可区别全色数
cycle
star
complete graph
corona graph
adjacent-vertex-distingushing total chromatic number