三正则构造图的邻点全和可区别全染色

吉林大学学报(理学版) ›› 2024, Vol. 62 ›› Issue (6): 1301-1307.

三正则构造图的邻点全和可区别全染色

杨超¹, 程银万¹, 姚兵²

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:2024-03-19 出版日期:2024-11-26 发布日期:2024-11-26
通讯作者: 杨超 E-mail:yangchao@sues.edu.cn

Neighbor Full Sum Distinguishing Total Coloring of 3-Regular Construction Graphs

YANG Chao¹, CHENG Yinwan¹, YAO Bing²

1. School of Mathematics, Physics and Statistics, Center of Intelligent Computing and Applied Statistics, Shanghai University of Engineering Science, Shanghai 201620, China;
2. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received:2024-03-19 Online:2024-11-26 Published:2024-11-26

摘要/Abstract

摘要： 首先, 根据Snark图的结构特点, 构造基于双星和十字交叉形的两类三正则图; 其次, 利用穷染法和组合分析法研究四类三正则构造图的邻点全和可区别全染色问题, 得到了它们的邻点全和可区别全色数均为2.

关键词: 非正常全染色, 邻点全和可区别全染色, 邻点全和可区别全色数, 三正则图

Abstract: Firstly, according to the structural characteristics of Snark graphs, we constructed two classes of 3-regular graphs based on Double Star and Cross. Secondly, we studied the problem of neighbor full sum distinguishing total coloring of four classes of 3-regular graphs by exhaustive coloring method and combinatorial analysis, and obtained that the neighbor full sum distinguishing total chromatic numbers for these graphs are all 2.

Key words: non-proper total coloring, neighbor full sum distinguishing total coloring, neighbor full sum distinguishing total chromatic number, 3-regular graph

中图分类号:

O157.5

杨超, 程银万, 姚兵. 三正则构造图的邻点全和可区别全染色[J]. 吉林大学学报(理学版), 2024, 62(6): 1301-1307.

YANG Chao, CHENG Yinwan, YAO Bing. Neighbor Full Sum Distinguishing Total Coloring of 3-Regular Construction Graphs[J]. Journal of Jilin University Science Edition, 2024, 62(6): 1301-1307.

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