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。
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.