带有最大平均度限制的图的邻和可区别全可选择数

doi:10.3969/j.issn.1000-5641.2022.01.002

华东师范大学学报（自然科学版） ›› 2022, Vol. 2022 ›› Issue (1): 10-16.doi: 10.3969/j.issn.1000-5641.2022.01.002

• 数学 • 上一篇

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^1,²()

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

收稿日期:2021-05-07 出版日期:2022-01-25 发布日期:2022-01-18
作者简介: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
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^1,²()

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:2021-05-07 Online:2022-01-25 Published:2022-01-18

摘要/Abstract

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 $\varDelta \left( G \right) + 3$ .

关键词: 组合零点定理, 邻和可区别全可选择数, 权转移法

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 $\varDelta \left( G \right) + 3$ .

Key words: Combinatorial Nullstellensatz, neighbor sum distinguishing total choice number, discharge method

中图分类号:

O157.5

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.

Donghan ZHANG. Neighbor sum distinguishing total choice number of graphs with bounded maximum average degree[J]. Journal of East China Normal University(Natural Science), 2022, 2022(1): 10-16.

参考文献 17

1	BONDY J A, MURTY U S R. Graph Theory with Applications [M]. New York: Macmilan Press Ltd, 1976.
2	PILŚNIAK M, WOŹNIAK M. On the total-neighbor-distinguishing index by sums. Graphs and Combinatorics, 2015, 31 (3): 771- 782. doi: 10.1007/s00373-013-1399-4
3	DONG A J, WANG G H. Neighbor sum distinguishing total colorings of graphs with bounded maximum average degree. Acta Mathematica Sinica (English Series), 2014, 30 (4): 703- 709. doi: 10.1007/s10114-014-2454-7
4	HOCQUARD H, PRZYBYŁO J. On the total neighbour sum distinguishing index of graphs with bounded maximum average degree. Journal of Combinatorial Optimization, 2020, 39, 412- 424. doi: 10.1007/s10878-019-00480-4
5	WANG J H, MA Q L, HAN X, et al. A proper total coloring distinguishing adjacent vertices by sums of planar graphs without intersecting triangles. Journal of Combinatorial Optimization, 2016, 32 (2): 626- 638. doi: 10.1007/s10878-015-9886-6
6	YANG D L, SUN L, YU X W, et al. Neighbor sum distinguishing total chromatic number of planar graphs with maximum degree 10. Applied Mathematics and Computation, 2017, 314, 456- 468. doi: 10.1016/j.amc.2017.06.002
7	QU C Q, WANG G H, WU J L, et al. On the neighbor sum distinguishing total colorings of planar graphs. Theoretical Computer Science, 2016, 609, 162- 170. doi: 10.1016/j.tcs.2015.09.017
8	SONG H J, PAN W H, GONG X N, et al. A note on the neighbor sum distinguishing total coloring of planar graphs. Theoretical Computer Science, 2016, 640, 125- 129. doi: 10.1016/j.tcs.2016.06.007
9	SONG W Y, DUAN Y Y, MIAO L Y. Neighbor sum distinguishing total coloring of IC-planar graphs. Discrete Mathematics, 2020, 343 (8): 111918. doi: 10.1016/j.disc.2020.111918
10	HAN M M, LU Y, LUO R, et al. Neighbor sum distinguishing total coloring of graphs with bounded treewidth. Journal of Combinatorial Optimization, 2018, 36, 23- 34. doi: 10.1007/s10878-018-0271-0
11	于筱蔚. 图的点可区别染色和标号 [D]. 济南: 山东大学, 2018.
12	QU C Q, DING L H, WANG G H, et al. Neighbor distinguishing total choice number of sparse graphs via the Combinatorial Nullstellensatz. Acta Mathematica Sinica (English Series), 2016, 32 (2): 537- 548. doi: 10.1007/s10255-016-0583-8
13	LU Y, XU C D, MIAO Z K. Neighbor sum distinguishing list total coloring of subcubic graphs. Journal of Combinatorial Optimization, 2018, 35, 778- 793. doi: 10.1007/s10878-017-0239-5
14	SUN L, YU G L, LI X. Neighbor sum distinguishing total choosability of 1-planar graphs with maximum degree at least 24. Discrete Mathematics, 2021, 344 (1): 112190. doi: 10.1016/j.disc.2020.112190
15	ZHANG D H, LU Y, ZHANG S G. Neighbor sum distinguishing total choice number of planar graphs without 6-cycles. Acta Mathematica Sinica (English Series), 2020, 36 (12): 1417- 1428. doi: 10.1007/s10114-020-0144-1
16	ZHANG D H, LU Y, ZHANG S G. Neighbor sum distinguishing total choosability of cubic graphs. Graphs and Combinatorics, 2020, 36, 1417- 1428.
17	ALON N. Combinatorial Nullstellensatz. Combinatorics Probability & Computing, 1999, (8): 7- 29.

[1]	韩鑫胤, 姚敏, 左连翠, 周伟娜. 几类图的字典式乘积图的(d,1)-全标号[J]. 华东师范大学学报(自然科学版), 2019, 2019(3): 35-41.
[2]	章溢, 刘志强, 邹思思, 温利民. 基于分层贝叶斯模型的损失准备金估计[J]. 华东师范大学学报(自然科学版), 2019, 2019(1): 13-23.
[3]	陈晓峰, 王艺桥. 最大度为7的哈林图的L(2,1)-标号[J]. 华东师范大学学报(自然科学版), 2019, 2019(1): 39-47,57.
[4]	师雪芹, 唐霞, 韦玉梅, 王健. 安徽省细鳞苔科植物物种多样性调查与研究[J]. 华东师范大学学报(自然科学版), 2018, 2018(4): 138-146.
[5]	张全锐, 刘建成. 欧氏空间中超曲面的L²调和2-形式[J]. 华东师范大学学报(自然科学版), 2018, 2018(3): 38-45.
[6]	苏亚攀, 潘海林, 赵振杰, 袁萌平. 磁偶极作用对铁基纳米晶条带LDGMI效应的影响[J]. 华东师范大学学报(自然科学版), 2018, 2018(3): 129-135,156.
[7]	孙慧, 姚兵. 探索Euler图的等价命题[J]. 华东师范大学学报(自然科学版), 2018, 2018(2): 23-30,40.
[8]	陈少军, 李晓涛, 郑军华. 蛋白酶体激活因子REGγ的肿瘤相关靶蛋白研究进展[J]. 华东师范大学学报(自然科学版), 2018, 2018(2): 125-130,159.
[9]	周枭潇, 毕春娟, 汪萌, 周雅, 陈振楼. 大气沉降对叶菜重金属的污染效应及其健康风险[J]. 华东师范大学学报(自然科学版), 2018, 2018(2): 141-150.
[10]	李艺春, 孙慧, 姚兵. 几种可扩散网络模型的边魔幻偶优美性[J]. 华东师范大学学报(自然科学版), 2018, 2018(1): 11-16,23.
[11]	董勇鹏, 王茜茹, 马娇娇. 一般时间终端一致连续多维BSDE解的稳定性[J]. 华东师范大学学报(自然科学版), 2018, 2018(1): 24-34,49.
[12]	杨琰琰, 魏文龙, 黄志刚. 几类微分与差分方程组的亚纯解[J]. 华东师范大学学报(自然科学版), 2018, 2018(1): 50-58.
[13]	马飞, 姚兵. 基于两种不同择优概率下的无标度网络模型[J]. 华东师范大学学报(自然科学版), 2017, 2017(6): 42-49.
[14]	马骅, 蒋雪中. 长江口潮周期内总悬浮颗粒物浓度的光学反演算法分析[J]. 华东师范大学学报(自然科学版), 2016, 2016(3): 146-155.
[15]	许洋. 非负特征图的列表不完全染色的研究(英)[J]. 华东师范大学学报(自然科学版), 2016, 2016(2): 51-55.

带有最大平均度限制的图的邻和可区别全可选择数

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

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献 17

相关文章 15

编辑推荐

Metrics

本文评价