吉林大学学报(理学版) ›› 2022, Vol. 60 ›› Issue (4): 833-837.

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关于哈林图的邻和可区别染色的注记

程银万1, 杨超1, 姚兵2   

  1. 1. 上海工程技术大学 数理与统计学院, 智能计算与应用统计研究中心, 上海 201620;
    2. 西北师范大学 数学与统计学院, 兰州 730070
  • 收稿日期:2021-10-10 出版日期:2022-07-26 发布日期:2022-07-26
  • 通讯作者: 杨超 E-mail:yangchao@sues.edu.cn

Notes on Neighbor Sum Distinguishing Coloring of Halin Graphs

CHENG Yinwan1, YANG Chao1, YAO Bing2   

  1. 1. Center of Intelligent Computing and Applied Statistics, School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China;
    2. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
  • Received:2021-10-10 Online:2022-07-26 Published:2022-07-26

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摘要： 用三种树染色算法和组合分析法, 完成对哈林图的邻和可区别边染色、 邻和可区别全染色以及邻点全和可区别全染色, 并证明1-2-3 猜想
和1-2猜想对哈林图均成立. 结果表明, 哈林图的邻点全和可区别全色数不超过3.

关键词: 1-2-3猜想, 1-2猜想, 邻点全和可区别全染色, 哈林图

Abstract: By using three types of tree coloring algorithms and combinatorial analysis, we completed the neighbor sum distinguishing edge coloring, the neighbor sum distinguishing total coloring and the neighbor full sum distinguishing total coloring of Halin graphs, and proved that the 1-2-3 conjecture and 1-2 conjecture were valid for Halin graphs. The results show that the neighbor full sum distinguishing total chromatic number of Halin graphs is not more than 3.

Key words: 1-2-3 conjecture, 1-2 conjecture, neighbor full sum distinguishing total coloring, Halin graph

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