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: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。

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 vertex distinguishing 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 χievt (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.