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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (6): 54-60.doi: 10.6040/j.issn.1671-9352.0.2020.592

• • 上一篇    

m个长为14的圈的不交并的点可区别Ⅰ-全染色

赵亚迪,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:2022-06-10
  • 作者简介:赵亚迪(1997— ),女,硕士研究生,研究方向为图论及其应用. E-mail:aady19970228@163.com*通信作者简介: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(11761064,61163037)

Vertex-distinguishing Ⅰ-total colorings of mC14

ZHAO Ya-di, CHEN Xiang-en*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2022-06-10

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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,证明mC14的最优点可区别Ⅰ-全染色及最优点可区别Ⅵ-全染色,确定图mC14的点可区别Ⅰ-全色数和点可区别Ⅵ-全色数。结论表明,点可区别Ⅰ-全染色猜想和点可区别Ⅵ-全染色猜想对图mC14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: The problems of the optimal vertex-distinguishing Ⅰ-total colorings(VDITC)and the optimal vertex-distinguishing Ⅵ-total colorings(VDVITC)of graph mC14 are proved by constructing a matrix which is composed of color sets and empty set as the elements and using the methods of distributing color sets in advance and describing coloring explicitly. Thus vertex-distinguishing Ⅰ-total chromatic numbers and the vertex-distinguishing Ⅵ-total chromatic numbers of graph mC14 are determined. The results show that the VDITC conjecture and VDVITC conjecture are valid for graph mC14.

Key words: 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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