图G的一个E-全染色是指使相邻点染以不同颜色且每条关联边与它的端点染以不同颜色的全染色.对图G的一个E-全染色f,一旦u,v∈V(G),u≠v,就有C(u)≠C(v),其中C(x)表示在f下点x的颜色以及与x关联的边的色所构成的集合,则f称为图G的点可区别的E-全染色,简称为VDET染色.令χe v t(G)=min{k|G存在k-VDET染色},称χe v t(G)为图G的点可区别E-全色数.在该文中,利用组合分析法、反证法并构造具体染色,讨论给出了完全二部图K 8,n(472≤n≤980)的点可区别E-全色数.
Let f be a proper total k-coloring of a simple graph G. For any vertex x ∈ V（G）, let Cf（x） denote the set of colors assigned to vertex x and the edges incident with x. If Cf（u） ≠ Cf（v） for all distinct vertices u and v of V（G）, then f is called a vertex- distinguishing total k-coloring of G. The minimum number k for which there exists a vertex- distinguishing total k-coloring of G is called the vertex-distinguishing total chromatic number of G and denoted by Xvt（G）. The vertex-disjoint union of two cycles of length n is denoted by 2Cn. We will obtain Xvt（2Cn） in this paper.
