完全二部图K_(5,n)的点可区别IE-全染色

Vertex distinguishing IE-total chromatic numbers of complete bipartite graph K_(5,n)

设G是简单图,图G的一个k-点可区别IE-全染色(简记为k-VDIET染色)f是指一个从V(G)∪E(G)到{1,2,…,k}的映射,且满足:uv∈E(G),有f(u)≠f(v);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-VDIET染色}称为图G的点可区别IE-全色数,记为χievt(G)。本文给出了完全二部图K5,n(n≥6)的点可区别IE-全色数。

Let G be a simple graph. An IE-total coloring f of G refers to a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. Let C （u） be the set of colors of vertex u and edges incident to u under f. For an IE- 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-ver- tex-distingnishing IE-total-coloring of G, or a k-VDIET coloring of G for short. The minimum number of colors required for a VDIET coloring of G is denoted by χvt^ie （G）, and it is called the VDIET chromatic number of G. VDIET chromatic numbers for the complete bipartite graph K5. n （ n≥ 6） were given.