完全二部图K_(8,n)(8≤n≤34)的点可区别E-全染色  

Vertex-distinguishing E-total coloring of complete bipartite graph K_(8,n) with 8≤n≤34

作　　者：杨澜 陈祥恩 YANG Lan;CHEN Xiang-en(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,甘肃兰州730070

出　　处：《高校应用数学学报（A辑）》2021年第4期492-500,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

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的颜色的全染色.对图G的一个E-全染色φ,一旦■u,v∈V(G),u≠v,就有C(u)≠C(v),其中C(x)表示在φ的作用下点x的颜色以及与x关联的边的色所构成的集合,则φ称为图G的点可区别的E-全染色(Vertex-Distinguishing E-Total Coloring),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.文中利用组合分析法,反证法及构造具体染色,讨论并给出了完全二部图K_(8,n)(8≤n≤34)的点可区别E-全色数.Let G be a simple graph.A total coloringφof 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 underφ,thenφis called a vertex-distinguishing E-total coloring of G.Letχ_(vt)^(e)(G)=min{k|G has a k-VDET coloring}.Thenχ_(vt)^(e)(G)is called the VDET chromatic number of G.The VDET coloring of complete bipartite graph K_(8,n) is discussed and the VDET chromatic number of K_(8,n)(8≤n≤34)has been obtained by using combinatorial analysis method,contradiction and constructing concrete coloring.

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]