完全二部图K5，n的点可区别IE-全染色

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：A↓uv∈E（G），有f（u）≠f（v）；A↓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χut^ie（G）。本文给出了完全二部图K5,n（n≥6）的点可区别IE-全色数。

Vertex distinguishing IE-total chromatic numbers of complete bipartite graph K5,n

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.