摘要
设f是图G的一个正常全染色.对任意x∈V(G),令C(x)表示与点x相关联或相邻的元素的颜色以及点x的颜色所构成的集合.若对任意u,v∈V(G),u≠v,有C(u)≠C(v),则称.f是图G的一个点强可区别全染色,对一个图G进行点强可区别全染色所需的最少的颜色的数目称为G的点强可区别全色数,记为X_(vst)(G).讨论了完全二部图K_(1,n),K_(2,n)和L_(3,n)的点强可区别全色数,利用组合分析法,得到了当n≥3时,X_(vst)(K_(1,n)=n+1,当n≥4时,X_(vst)(K_(2,n)=n+2,当n≥5时,X_(vst)(K_(3,n))=n+2.
Let f be a proper total coloring of G. For each x E V（G）, let C（x） denote the set of all colors of the elements incident with or adjacent to x and the color of x. If u, v ∈ V（G）, u ≠ v, we have C（u） ≠C（v）, then f is called a vertex strongly distinguishing total coloring of G. The minimum number k for which there exists a vertex strongly distinguishing total coloring of G using k colors is called the vertex strongly distinguishing total chromatic number of G and denoted by Хvst（G）. In this paper, we discuss vertex strongly distinguishing total chromatic numbers of complete bipartite graphs K1,n, K2,n and K3,n, using methods of combinatorial analysis, obtained that Хvst（K1,n） = n ＋ 1 when n 〉 3, Хvst（K2,n） = n ＋ 2 when n ≥ 4,Хvst（K3,n） = n＋ 2 when n ≥ 5.
出处
《数学的实践与认识》
CSCD
北大核心
2012年第11期214-218,共5页
Mathematics in Practice and Theory
基金
国家自然科学基金(61163037
61163054)
西北师范大学"知识与科技创新工程"项目(nwnu-kjcxgc-03-61)
宁夏自然基金(NZ1154)
宁夏大学科学研究基金((E):ndzr10-7)
关键词
完全二部图
正常全染色
点强可区别全染色
点强可区别全色数
complete bipartite graphs
proper total coloring
vertex strongly distinguishing total coloring
vertex strongly distinguishing total chromatic number
