JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (6): 35-39.doi: 10.6040/j.issn.1671-9352.0.2022.220

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A new method of neighbor sum distinguishing total coloring of graphs

Jingzhi CHANG1(),Chao YANG1,*(),Bing YAO2   

  1. 1. School of Mathematics, Physics and Statistics, Shanghai University ofEngineering Science, Shanghai 201620, China
    2. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2022-04-18 Online:2023-06-20 Published:2023-05-23
  • Contact: Chao YANG E-mail:changjingzhi1@163.com;yangchao@sues.edu.cn

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Abstract:

The neighbor sum distinguishing 2-total coloring of a tree is presented along with the independence of the minimum decycling set of a 3-regular graph and the acyclicity of the corresponding decycling subgraphs. This method provides a simple way to prove that the neighbor sum distinguishing total chromatic number of a 3-regular graph satisfies the 1-2 Conjecture. The independent decycling set method is used to determine the neighbor sum distinguishing total chromatic number of an r-regular graph, Halin graph, and Cartesian product graph of paths.

Key words: non-proper total coloring, decycling set, neighbor sum distinguishing total coloring, 1-2 Conjecture

CLC Number: 

  • O157.5
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