当35 ≤ d ≤ 55时圈的d-强全染色

黄小佳; 陈祥恩; 王治文

当35 ≤ d ≤ 55时圈的d-强全染色

1.
西北师范大学~~数学与统计学院, 兰州 730070;
2.
宁夏大学~~数学计算机科学学院, 银川 750021

基金项目:

国家自然科学基金,(61163037, 61163054,11261046, 61363060); 宁夏回族自治区百人计划

详细信息

作者简介:
黄小佳, 女, 硕士研究生,研究方向为图论及其应用

通讯作者:
黄小佳, 女, 硕士研究生,研究方向为图论及其应用. E-mail: huangxiaojianwnu@126.com

中图分类号: O157.5
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出版历程
- 收稿日期: 2014-09-09
- 刊出日期: 2015-11-25

d-strong total colorings of cycles when 35<=d<=55

摘要

摘要: 对于图G=(V,E)的一个正常全染色, 用C(v)表示顶点v\in V的颜色以及与 v 关联的边的颜色构成的集合, 称之为点v\in V的色集合. 如果 C(u)\neq C(v), 那么就说u和v被该全染色所区别.一个图 G的 d-强全染色是指使得满足 1\leq d_{G}(u,v)\leq d的任意一对顶点 u 和 v 可区别的一个正常全染色. 所谓一个图 G 的d-强全色数是指对图 G 进行d-强全染色所需要的颜色的数目的最小值. 文中对当$d\in [35,55]$时圈的 d-强全色数进行了确定.
- 正常全染色 /
- d-强全染色 /
- d-强全色数 /
- 圈
Abstract: For a proper total coloring of a graph G=(V,E), thepalette C(v) of a vertex v\in V is the set of the colors of the edges incident with v and the color of the vertex itself. If C(u)\neq C(v), then the two vertices u and v of G are said to be distinguished by the total coloring. A d-strong total coloring of G is a proper total coloring that distinguishes all pairs of verticeu and vwith distance 1\leq d_{G}(u,v)\leq d. The d-strong total chromatic number chi^{''}_{d}(G) of Gis the minimum number of colors of a d-strong total coloring ofG. In this paper we determine \chi^{''}_{d}(C_{n}) completely for cycles where d\in [35,55]$ and $d\in \textbf{N

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参考文献(1)

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