完全二部图K3,n(n≥18)的点可区别E-全染色
Vertex-Distinguishing E-Total coloring of complete bipartite graph K3,n with n≥18

摘要： G是一个简单图, G 的一个E-全染色f是指使相邻点着不同色且每条关联边与它的端点着以不同的色的全染色。 设 f 为 G 的一个E-全染色。 对任意点x∈V(G), 用C(x)表示在 f 下点 x 的色以及与 x 关联的边的颜色所构成的集合。 若 ∠u,v∈V(G),u≠v, 有C(u)≠C(v), 则 f 称为是图G的点可区别的E-全染色, 简称为VDET染色。 图G的VDET染色所用颜色数目的最小值称为图 G 的点可区别E-全色数或简称为 VDET 色数, 记为χevt(G)。讨论并给出了完全二部图K3,n(n≥18)的点可区别E-全色数。
Abstract: Let G be a simple graph. A total coloring f of G is called an E-total coloring if no two adjacent vertices of G receive the same color, and no edge of G receives the same color as one of its endpoints. For an E-total coloring f of a graph G and any vertex x of G, let C(x)denote the set of colors of vertex x and of the edges incident with x, we call C(x)the color set of x. If C(u)≠C(v)for any two different vertices u and v of V(G), then we say that f is a vertex-distinguishing E-total coloring of G or a VDET coloring of G for short。 The minimum number of colors required for a VDET coloring of G is denoted by χevt(G)and is called the VDET chromatic number of G. The VDET coloring of complete bipartite graph K3,n is discussed in paper and the VDET chromatic number of K3,n(n≥18)has been obtained