当35 ≤ d ≤ 55时圈的d-强全染色

华东师范大学学报(自然科学版) ›› 2015, Vol. 2015 ›› Issue (6): 30-35.

当35 ≤ d ≤ 55时圈的d-强全染色

黄小佳, 陈祥恩, 王治文

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

收稿日期:2014-09-09 出版日期:2015-11-25 发布日期:2015-12-23
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 E-mail: huangxiaojianwnu@126.com
作者简介:黄小佳, 女, 硕士研究生,研究方向为图论及其应用
基金资助:
国家自然科学基金,(61163037, 61163054,11261046, 61363060); 宁夏回族自治区百人计划

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

HUANG Xiao-Jia, CHEN Xiang-恩, WANG Zhi-Wen

Received:2014-09-09 Online:2015-11-25 Published:2015-12-23

摘要/Abstract

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.

关键词: 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

中图分类号:

O157.5

黄小佳, 陈祥恩, 王治文. 当35 ≤ d ≤ 55时圈的d-强全染色[J]. 华东师范大学学报(自然科学版), 2015, 2015(6): 30-35.

HUANG Xiao-Jia, CHEN Xiang-恩, WANG Zhi-Wen. d-strong total colorings of cycles when 35<=d<=55[J]. Journal of East China Normal University(Natural Sc, 2015, 2015(6): 30-35.

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