图mC15的点可区别Ⅰ-全染色和Ⅵ-全染色

吉林大学学报(理学版) ›› 2021, Vol. 59 ›› Issue (3): 497-512.

图mC₁₅的点可区别Ⅰ-全染色和Ⅵ-全染色

赵亚迪, 陈祥恩

西北师范大学数学与统计学院, 兰州 730070

收稿日期:2020-10-30 出版日期:2021-05-26 发布日期:2021-05-23
通讯作者: 陈祥恩 E-mail:chenxe@nwnu.edu.cn

Vertex-Distinguishing Ⅰ-Total Colorings and Vertex-Distinguishing Ⅵ-Total Colorings of Graph mC₁₅

ZHAO Yadi, CHEN Xiang’en

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received:2020-10-30 Online:2021-05-26 Published:2021-05-23

摘要/Abstract

摘要： 通过构造以色集合和空集为元素的矩阵, 利用色集合事先分配法及构造具体染色的方法, 解决了图mC₁₅的最优点可区别Ⅰ-全染色及最优点可区别Ⅵ-全染色问题, 得到了图mC₁₅的点可区别Ⅰ-全色数和点可区别Ⅵ-全色数. 结果表明, 点可区别Ⅰ-全染色猜想和点可区别Ⅵ-全染色猜想对图mC₁₅成立.

关键词: 点可区别Ⅰ-全染色, 点可区别Ⅵ-全染色, 点可区别Ⅰ-全色数, 点可区别Ⅵ-全色数

Abstract: We solved the problems of the optimal vertex-distinguishing Ⅰ-total colorings (VDITC) and the optimal vertex-distinguishing Ⅵ-total colorings (VDVITC) of graph mC₁₅ by constructing a matrix with color sets and empty set as its elements, and using the methods of distributing color sets in advance and describing coloring explicitly, and obtained vertex-distinguishing Ⅰ-total chromatic numbers and the vertex-distinguishing Ⅵ-total chromatic numbers of graph mC₁₅. The results show that the VDITC conjecture and VDVITC conjecture are valid for graph mC₁₅.

Key words: vertex-distinguishing Ⅰ-total colorings, vertex-distinguishing Ⅵ-total colorings, vertex-distinguishing Ⅰ-total chromatic numbers, vertex-distinguishing Ⅵ-total chromatic numbers

中图分类号:

O157.5

赵亚迪, 陈祥恩. 图mC₁₅的点可区别Ⅰ-全染色和Ⅵ-全染色[J]. 吉林大学学报(理学版), 2021, 59(3): 497-512.

ZHAO Yadi, CHEN Xiang’en. Vertex-Distinguishing Ⅰ-Total Colorings and Vertex-Distinguishing Ⅵ-Total Colorings of Graph mC₁₅[J]. Journal of Jilin University Science Edition, 2021, 59(3): 497-512.

图mC₁₅的点可区别Ⅰ-全染色和Ⅵ-全染色

Vertex-Distinguishing Ⅰ-Total Colorings and Vertex-Distinguishing Ⅵ-Total Colorings of Graph mC₁₅

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