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《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (11): 76-82.doi: 10.6040/j.issn.1671-9352.0.2020.362

• • 上一篇    

mC7的点可区别Ⅰ-全染色和Ⅵ-全染色

杨晗,陈祥恩*   

  1. 西北师范大学数学与统计学院, 甘肃 兰州 730070
  • 发布日期:2021-11-15
  • 作者简介:陈祥恩(1965— ), 男, 教授, 研究方向为图论及其应用. E-mail:chenxe@nwnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11761064)

Vertex-distinguishing Ⅰ-total colorings and vertex-distinguishing Ⅵ-total colorings of mC7

YANG Han, CHEN Xiang-en*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2021-11-15

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摘要： 利用色集合事先分配法及具体的染色给出了mC7的最优点可区别Ⅰ-全染色以及最优点可区别Ⅵ-全染色,进而确定了图mC7的点可区别Ⅰ-全色数及点可区别Ⅵ-全色数。结论表明VDITC猜想和VDVITC猜想对图mC7成立。

关键词: 圈, 不交并, 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: By using the methods of constructing a matrix which was composed of color sets and empty set as the elements, distributing color sets in advance and coloring explicitly, to give the optimal vertex distinguishing Ⅰ-total colorings and the optimal vertex distinguishing Ⅵ-total colorings of mC7. Thus vertex distinguishing Ⅰ-total chromatic numbers and the vertex distinguishing Ⅵ-total chromatic numbers of mC7 are determined. The results show that the VDITC conjecture and VDVITC conjecture are valid for mC7.

Key words: cycle, disjoint union, vertex-distinguishing Ⅰ-total coloring, vertex-distinguishing Ⅵ-total coloring, vertex-distinguishing Ⅰ-total chromatic number, vertex-distinguishing Ⅵ-total chromatic number

中图分类号: 

  • O157.5
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