完全二部图K3,n（3≤n≤17）的点可区别E-全染色

摘要

Let G be a simple graph,f is a total coloring of G.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 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 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 χe vt (G)and is called the VDET chromatic number of G.Based on the analytical method and proof by contradiction,the VDET coloring of complete bipartite graph K 3 ,n was discussed and the VDET chromatic number of K 3 ,n (3≤n≤17)was obtained.%设 G 是一个简单图,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 关联边颜色所构成的集合。若∀u,v∈V (G),u≠v,有 C(u)≠C(v),则f 称为图G 的点可区别 E-全染色,简称 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(简称为 VDET 色数),记为χe vt (G)。利用分析法和反证法,讨论并给出完全二部图 K 3,n (3≤n≤17)的点可区别 E-全色数。