一类仙人掌图的D(2)-点可区别全染色

吉林大学学报(理学版) ›› 2024, Vol. 62 ›› Issue (1): 1-0006.

• • 下一篇

一类仙人掌图的D(2)-点可区别全染色

汪银芳¹, 李沐春¹, 王国兴²

1. 兰州交通大学应用数学研究所, 兰州 730070; 2. 兰州财经大学信息工程学院, 兰州 730020

收稿日期:2023-04-14 出版日期:2024-01-26 发布日期:2024-01-26
通讯作者: 李沐春 E-mail:limuchunmath@163.com

D(2)-Vertex-Distinguishing Total Colorings of a Class of Cactus Graphs

WANG Yinfang¹, LI Muchun¹, WANG Guoxing²

1. Institute of Applied Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China;
2. School of Information Science and Engineering, Lanzhou University of Finance and Economics, Lanzhou 730020, China

Received:2023-04-14 Online:2024-01-26 Published:2024-01-26

摘要/Abstract

摘要： 用数学归纳法和组合分析法给出最大度为3的仙人掌图G_T的D(2)-点可区别全染色, 进而得到χ_2vt(G_T)≤6. 结果表明, D(β)-VDTC猜想对最大度为3的仙人掌图成立.

关键词: 仙人掌图, D(2)-点可区别全染色, D(2)-点可区别全色数

Abstract: By applying mathematics induction and combinatorial analysis, we gave D(2)-vertex-distinguishing total colorings of cactus graphs G_T with maximum degree of 3, and then obtained χ_2vt(G_T)≤6. The result shows that D(β)-VDTC conjecture holds for cactus graphs with maximum degree of 3.

Key words: cactus graph, D(2)-vertex-distinguishing total cocoring, D(2)-vertex-distinguishing total chromatic number

中图分类号:

O157.5

汪银芳, 李沐春, 王国兴. 一类仙人掌图的D(2)-点可区别全染色[J]. 吉林大学学报(理学版), 2024, 62(1): 1-0006.

WANG Yinfang, LI Muchun, WANG Guoxing. D(2)-Vertex-Distinguishing Total Colorings of a Class of Cactus Graphs[J]. Journal of Jilin University Science Edition, 2024, 62(1): 1-0006.

一类仙人掌图的D(2)-点可区别全染色

D(2)-Vertex-Distinguishing Total Colorings of a Class of Cactus Graphs

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