κ-树及其邻点可区别全染色  

The Adjacent Vertex-distinguishing Total coloring of κ-tree

作　　者：张琛[1] 李红霞[1] ZHANG Chen LI Hong-Xia(School of Mathematics and Statistics, Longdong University, Qingyang 745000, Gans)

机构地区：[1]陇东学院数学与统计学院,甘肃庆阳745000

出　　处：《陇东学院学报》2017年第1期11-14,共4页Journal of Longdong University

基　　金：甘肃省高等学校科研项目<模糊图在网络优化中的应用研究>(2015A-144)

摘　　要：G是一个简单图,G的一个全染色f是指使相邻顶点和相邻边着不同颜色且每条关联边与它的顶点着以不同颜色的全染色。设f为图G一个全染色,对任意x∈V(G),用C(x)表示在f下顶点的颜色以及与x关联的边的颜色所构成的集合。若任意uv∈E(G),u≠v,有C(u)≠C(v),则称f是图G的邻点可区别的全染色,该问题的主要目的是确定图G的邻点可区别全色数。基于树的基本结构,构造了一种新的图类—κ-树,讨论并给出了两类κ-树S(n,1),S(n,2)的邻点可区别全色数。Let G be a simple graph.A total coloring f of G is called an total coloring if no two adjacent vertices and no two adjacent edges of G receive the same color,and no edge of receives the same color as one of its endpoints.For an total coloring f of a graph and any vertex 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 adjacent vertexes u and v of V（G）,then we say that f is a adjacent vertex-distinguishing total coloring of G.The main purpose of this problem is to determine the adjacent vertex-distinguishing total chromatic number of G.In this paper,a new graph,κ-tree,is constructed on the base of the structure of the tree.The adjacent vertex-distinguishing total chromatic number on κ-tree are obtained for some special graphs,such as S（n,1） and S（n,2）.

关 键 词：树 κ-树 邻点可区别全染色 邻点可区别全色数 

分 类 号：O157.5[理学—数学]