摘要
设G是简单图,图G的一个k-点可区别Ⅵ-全染色(简记为k-VDIVT染色),f是指一个从V(G)∪E(G)到{1,2,…,k}的映射,满足:()uv,uw∈E(G),v≠w,有,f(uv)≠f(uw);()u,V∈V(G),u≠v,有C(u)≠C(v),其中C(u)={f(u)}∪{f(uv)|uv∈E(G)}.数min{k|G有一个k-VDIVT染色}称为图G的点可区别Ⅵ-全色数,记为x_(vt)^(iv)(G).讨论了完全图K_n及完全二部图K_(m,n)的VDIVT色数.
Let G be a simple graph.An IV-total coloring f of G refers to a coloring of the vertices and edges of G so that no two adjacent edges receive the same color.Let C（u） be the set of colors of vertex u and edges incident to u under f.For anⅣ-total coloring f of G using k colors,if C（u）≠C（v） for any two different vertices u and v of V（G）,then f is called a k-vertex-distinguishingⅣ-total-coloring of G,or a k-VDIVT coloring of G for short.The minimum number of colors required for a VDIVT coloring of.G is denoted by x_（vt）^（iv）（G）,it is called the VDIVT chromatic number of G.In this paper,we have get the VDIVT chromatic numbers of complete graph K_n and complete bipartite graph K_（m,n）
出处
《数学的实践与认识》
CSCD
北大核心
2012年第6期233-236,共4页
Mathematics in Practice and Theory
基金
国家自然科学基金(61163037
61163054)
兰州商学院2011年度重点科研项目(LZ201121)
关键词
图
Ⅳ-全染色
点可区别Ⅳ-全染色
点可区别Ⅳ-全色数
graphs
IV-total coloring
vertex-distinguishing IV-total coloring
vertex-distin guishing IV-total chromatic number
