完全二部图K9,n(93≤n≤216)的点可区别E-全染色  

Vertex-distinguishing E-total coloring of a complete bipartite graph K(93 ≤ n ≤ 216)

作　　者：陈祥恩 杨伟光 CHEN Xiang'en;YANG Weiguang(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《华东师范大学学报（自然科学版）》2020年第6期24-29,共6页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(11761064,61163037)。

摘　　要：图G的一个E-全染色是指使相邻点染以不同颜色且每条关联边与它的端点染以不同颜色的全染色.对图G的一个E-全染色f,一旦■u,v∈V(G),u≠v,就有C(u)≠C(v),其中C(x)表示在f下点x的颜色以及与x关联的边的颜色所构成的集合,则f称为图G的点可区别的E-全染色,简称VDET染色.令χvte(G)=min{k:G存在k-VDET染色},称χvte(G)为图G的点可区别E-全色数.本文利用反证法、组合分析法及构造具体染色等方法,讨论并给出了完全二部图K9,n(93≤n≤216)的点可区别E-全色数.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,if C(u)≠C(v) for any two distinct vertices u and v of V(G),where C(x) denotes the set of colors of vertex x and of the edges incident with x under f,then f is called a vertex-distinguishing E-total coloring of G.Let χvte(G)=min{k:G has a k-VDET coloring}.Then,χvte(G) is called the VDET chromatic number of G.By using contradiction,the method of a combinatorial analysis and the method of constructing specific coloring,the VDET coloring of a complete bipartite graph K9,n is discussed and the VDET chromatic number of K9,n(93≤n≤216) is determined.

关 键 词：完全二部图 E-全染色 点可区别E-全染色 点可区别E-全色数 

分 类 号：O157.5[理学—数学]