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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2018, Vol. 35 ›› Issue (1): 69-78.doi: 10.3969/j.issn.1005-3085.2018.01.007

• • 上一篇    下一篇

一些特殊Corona图的$b$-连续性

吕   闯1,   王科伦2,   张若东1,   潘淑霞1   

  1. 1- 吉林医药学院数学教研室，吉林  132013
    2- 大连海事大学数学系，大连  116026
  • 收稿日期:2015-08-03 接受日期:2017-06-28 出版日期:2018-02-15 发布日期:2018-04-15
  • 基金资助:
    国家自然科学基金(61472058).

The $b$-continuity of Some Special Corona Graphs

LV Chuang1,   WANG Ke-lun2,   ZHANG Ruo-dong1,   PAN Shu-xia1   

  1. 1- Department of Mathematics, Jilin Medical University, Jilin 132013
    2- Department of Mathematics, Dalian Maritime University, Dalian 116026
  • Received:2015-08-03 Accepted:2017-06-28 Online:2018-02-15 Published:2018-04-15
  • Supported by:
    The National Natural Science Foundation of China (61472058).

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摘要： 图$G$的$b$-染色是一个正常顶点染色，且在每两个色类之间至少存在一条边．图$G$的$b$-染色数是最大的整数$k$，满足用$k$种颜色能对$G$进行$b$-染色，记为$b(G)$．一个图$G$称为$b$-连续的当且仅当对于每个正整数$k$，$\chi(G)\leq k \leq b(G)$，图$G$存在一个$(k)b$-染色．本文根据Corona图的结构性质，通过设计具体染色方案的方法，证明了一些特殊Corona图的$b$-连续性．

关键词: $b$-染色, $b$-染色数, $b$-连续, $m$-度, Corona图

Abstract: The $b$-coloring of a graph $G$ is a proper vertex coloring, in which every two color classes exists at least one edge. The $b$-chromatic number of a graph $G$ is the largest integer $k$ such that $G$ admits a $b$-coloring with $k$ colors. A graph $G$ is said to be $b$-continuity if and only if for every integer $k$, $\chi(G) \leq k \leq b(G)$, there exists a $b$-coloring with $k$ colors. In this paper, the $b$-continuity of some special Corona graphs is proved by designing the specific coloring scheme according to the structural properties of Corona graphs.

Key words: $b$-coloring, $b$-chromatic number, $b$-continuity, $m$-degree, Corona graph

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