数学

带有最大平均度限制的图的邻和可区别全可选择数

  • 张东翰
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  • 1. 西北工业大学 数学与统计学院, 西安 710129
    2. 商洛学院 数学与计算机应用学院, 陕西 商洛 726000
张东翰, 男, 博士, 副教授, 研究方向为图论及其应用. E-mail: zhang_dh@mail.nwpu.edu.cn

收稿日期: 2021-05-07

  网络出版日期: 2022-01-18

基金资助

陕西省科协高校青年人才托举计划(20180508)

Neighbor sum distinguishing total choice number of graphs with bounded maximum average degree

  • Donghan ZHANG
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  • 1. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China
    2. School of Mathematics and Computer Application, Shangluo University, Shangluo Shaanxi 726000, China

Received date: 2021-05-07

  Online published: 2022-01-18

摘要

利用组合零点定理和权转移法, 研究了最大度 $\varDelta \left( G \right) \geqslant 8$ 且最大平均度 ${\rm{mad}}\left( G \right) < \frac{{14}}{3}$ 的图 $G$ 的邻和可区别列表全染色, 确定了该类图的邻和可区别全可选择数不超过 $\varDelta \left( G \right) + 3$ .

本文引用格式

张东翰 . 带有最大平均度限制的图的邻和可区别全可选择数[J]. 华东师范大学学报(自然科学版), 2022 , 2022(1) : 10 -16 . DOI: 10.3969/j.issn.1000-5641.2022.01.002

Abstract

This paper explores the neighbor sum distinguishing list total coloring of graphs $G$ with maximum degree $\varDelta \left( G \right) \geqslant 8$ and maximum average degree ${\rm{mad}}\left( G \right) < \frac{{14}}{3}$ . By applications of the Combinatorial Nullstellensatz and discharge method, moreover, it is shown that the neighbor sum distinguishing total choice number of the graphs does not exceed $\varDelta \left( G \right) + 3$ .

参考文献

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