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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2021, Vol. 38 ›› Issue (5): 721-730.doi: 10.3969/j.issn.1005-3085.2021.05.011

• • 上一篇    下一篇

路与几类图的 Cartesian 积的邻点扩展和可区别全染色

王国兴1,2   

  1. 1. 兰州财经大学丝绸之路经济研究院，兰州 730020
    2. 兰州财经大学信息工程学院，兰州 730020
  • 出版日期:2021-10-15 发布日期:2021-12-15
  • 基金资助:
    国家自然科学基金 (11761064; 61662066)；甘肃省高等学校创新基金 (2021B-148)；兰州财经大学丝绸之路经济研究院重点项目 (JYYZ201903)；兰州财经大学重大招标项目 (lzufe2020a-01)；兰州财经大学高等教育教学改革研究重点项目 (LJZ201908).

Neighbor Expanded Sum Distinguishing Total Colorings of Some Cartesian Product Graphs

WANG Guoxing1,2   

  1. 1. Gansu Silk Road Economic Research Institute, Lanzhou University of Finance and Economics, Lanzhou 730020
    2. College of Information Engineering, Lanzhou University of Finance and Economics, Lanzhou 730020
  • Online:2021-10-15 Published:2021-12-15
  • Supported by:
    The National Natural Science Foundation of China (11761064; 61662066); the Innovation Foundation of Universities in Gansu Province (2021B-148); the Key Topics of the Silk Road Economic Research Institute of Lanzhou University of Finance and Economics (JYYZ201903); the Major Bidding Project of Lanzhou University of Finance and Economics (lzufe2020a-01); the Key Research Projects of Higher Education Reform in Lanzhou University of Finance and Economics (LJZ201908).

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摘要：

本文通过对图的 Cartesian 积的结构进行分析，应用构造染色模式的方法证明了 Cartesian 积 $P_m\Box C_n$、$P_m\Box W_{n} (n\geq 9)$、$P_m\Box K_n$ 这几类的邻点扩展和可区别全色数 (NESDTC) 均为 2．由此说明 Flandrin 等人提出的 NESDTC 猜想对于 Cartesian 积 $P_m\Box C_n$、$P_m\Box W_{n} (n\geq 9)$ 和 $P_m\Box K_n$ 是成立的．

关键词: $k$-全染色, Cartesian 积, 邻点扩展和可区别全染色, 邻点扩展和可区别全色数

Abstract:

Based on the structure of Cartesian product graphs, we apply the constructional coloring functions to prove that the neighbor expanded sum distinguishing total chromatic indexes (NESDTC) of graphs $P_m\Box C_n$, $P_m\Box W_{n} (n\geq 9)$ and $P_m\Box K_n$ equal to 2. Those results show that the NESDTC-conjecture proposed by Flandrin {\sl et al} is correct for graphs $P_m\Box C_n$, $P_m\Box W_{n} (n\geq 9)$ and $P_m\Box K_n$.

Key words: $k$-total coloring, Cartesian product, neighbor expanded sum distinguishing total coloring, neighbor expanded sum distinguishing total chromatic index

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