边替换图的邻和可区别全染色

吉林大学学报(理学版) ›› 2023, Vol. 61 ›› Issue (3): 477-482.

边替换图的邻和可区别全染色

常景智¹, 杨超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:2022-07-19 出版日期:2023-05-26 发布日期:2023-05-26
通讯作者: 杨超 E-mail:yangchao@sues.edu.cn

Neighbor Sum Distinguishing Total Colorings of Edge-Replaced Graphs

CHANG Jingzhi¹, YANG Chao¹, YAO Bing²

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:2022-07-19 Online:2023-05-26 Published:2023-05-26

摘要/Abstract

摘要： 考虑图的邻和可区别全染色问题及其相关的1-2猜想. 首先, 利用独立消圈集法得到剖分图S(G)和三角扩展图R(G)的邻和可区别全色数；其次, 当G为任意简单连通图且T为给定的特殊图时, 证明边替换图G［T］满足1-2猜想.

关键词: 边替换图, 独立消圈集法, 邻和可区别全色数, 1-2猜想

Abstract: We considered the problem of neighbor sum distinguishing total colorings of gragh and its related 1-2 conjecture. Firstly, by using the independent decycling set method, we obtained the neighbor sum distinguishing total chromatic numbers of the subdivision graph S(G) and the triangular extension graph R(G). Secondly, when G was an arbitrary simple connected graph and T was a given special graph, we proved that the edge-replaced graph G［T］ satisfied the 1-2 conjecture.

Key words: edge-replaced graph, independent decycling set method, neighbor sum distinguishing total chromatic number, 1-2 conjecture

中图分类号:

O157.5

常景智, 杨超, 姚兵. 边替换图的邻和可区别全染色[J]. 吉林大学学报(理学版), 2023, 61(3): 477-482.

CHANG Jingzhi, YANG Chao, YAO Bing. Neighbor Sum Distinguishing Total Colorings of Edge-Replaced Graphs[J]. Journal of Jilin University Science Edition, 2023, 61(3): 477-482.