奇数阶Halin图的边覆盖染色  

On Edge-cover Coloring of Halin Graph on Odd Order

作　　者：高淑娥 

机构地区：[1]北京交通职业技术学院基础部,北京102200

出　　处：《吉林师范大学学报（自然科学版）》2013年第3期127-129,共3页Journal of Jilin Normal University:Natural Science Edition

摘　　要：设图G(V,E)是简单图,其中V(G)和E(G)是图的顶点集和边集.C是边集E到集合{1,2,…,k}的映射:C:E→{1,2,…,k},称C是图G的k-边染色.令Ci(v)为染色C中与顶点v关联的i色边的数目.若对V中每个顶点v及每种颜色i∈{1,2,…,k}都有Ci(v)≥1,则称C为图G的边覆盖染色.使G有边覆盖染色所需最大k称为图G的边覆盖色数,用χ'c(G)表示.对简单图已知δ-1≤χ'C(G)≤δ,χ'C(G)=δ的图称为CI类图,否则称为CⅡ类图.讨论了基于边覆盖色数的奇数阶Halin图的分类问题.Let G（V,E） be a simple graph with vertex set V（G） and edge set E（G）.C is a mapping from E（G） to { 1,2,…,k},that is C： E→{ 1,2,…,k},C is called a k-edge-coloring of G.Let Ci（v） be the number of edges of G incident with vertex v receiving color i in coloring C.C is called a k-edge cover-coloring of G if Ci（v） ≥1 for each v∈V,and i ∈{ 1,2,…,k}.The maximum positive integer k for which G has a k-edge cover-coloring is called the edge cover chromatic index of G.It is denoted by χ＇C（G）.For simple graph,it is known that δ-1≤ χ＇C（G） ≤δ.G is of class CI if χ＇C（G） = δ,otherwise G is of class CⅡ.We discuss the classification of Halin graph on odd order based on the edge cover chromatic index.

关 键 词：边染色 边覆盖染色 HALIN图 

分 类 号：O157.6[理学—数学]