完全二部图K_(9,n)的点可区别IE-全染色(英文)

Vertex-distinguishing IE-total colorings of complete bipartite graphs K_(9,n)

G是一个简单图,G的一个IE全染色f是一个映射,该映射满足:对u,v∈V(G),u≠v,有C(u)≠C(v).图G的一个点可区别IE-全染色f是指一个从V(G)∪E(G)到{1,2,…,k}的映射,且满足:对uv∈E(G),有f(u)≠f(v);对u,v∈V(G),u≠v,有C(u)≠C(v),其中C(u)={f(u)}∪{f(uv):uv∈E(G)},简称k-VDIET.数min{k:G有一个k-VDIET染色}称为图G的点可区别IE-全色数或简称VDIET色数,记为χievt(G).本文讨论并给出了完全二部图K9,n的点可区别IE-全色数.

Let G be a simple graph . An IE-total coloring f of G is a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color . For each vertex x of G , let C（x） be the set of colors of vertex x and edges incident to x under f . A k-vertex-distinguishing IE-total-coloring of G is an IE-total coloring f of G（a k-VDIET coloring of G for short） using k colors ,if C（u）≠ C（v） for any two different vertices u and v of G .The minimum number of colors required for a VDIET coloring of G is denoted by χievt （G） , and is called vertex-distinguishing IE-total chromatic number or the VDIET chromatic number of G briefly . VDIET colorings of complete bipartite graphs K9 ,n is discussed in this paper and the VDIET chromatic number of K9 ,n has been obtained .