完全二部图K_(10,n)(215≤n≤466)的点可区别E-全染色

图G的一个E-全染色是指使相邻点染以不同的颜色,且每条关联边和它的端点染以不同的颜色的全染色。对图G的一个E-全染色f,一旦对图G中任意互不相同的两点u, v,有C(u)≠C(v),其中C(x)表示在f下点x的颜色以及与x关联的边的色所构成的集合,那么f称为图G的点可区别的E-全染色,简称为VDET染色。令χ_(vt)~e(G)=min{k|G存在k-VDET染色},称χ_(vt)~e(G)为图G的点可区别E-全色数。运用分析法和反证法,讨论并证明了完全二部图K_(10,n)(215≤n≤466)的点可区别E-全色数。

Vertex-distinguishing E-total coloring of complete bipartite graph K 10, n with 215 ≤ n ≤ 466.

Let G be a simple graph. A total coloring f of G is called an E-total coloring if any two adjacent vertices of G receive different colors, and any edge of G receives the color different from those of its endpoints. Let C(x) denote the set of colors of vertex x and of the edges incident with x under f for an E-total coloring f of a graph G, if C(u)≠ C(v) for any two distint vertice u and v of V（G）,then f is called a vertex-distinguishing E-total coloring of G. Let χ_vt ^e(G)=min{k G has a k-VDET coloring}, Then χ_vt ^e(G) is called the VDET chromatic number of G. By using analytical method and proof by contradiction, the VDET coloring of complete bipartite graph K_10n is investigated and the VDET chromatic number of K _{10, n} (215 ≤ n ≤ 466) has been obtained.