您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (2): 47-52, 58.doi: 10.6040/j.issn.1671-9352.0.2022.347

•   • 上一篇    下一篇

树图的2-距离和可区别染色

刘欢1(),强会英1,*(),王洪申2,白羽1   

  1. 1. 兰州交通大学数理学院，甘肃 兰州 730070
    2. 兰州理工大学机电工程学院, 甘肃 兰州 730050
  • 收稿日期:2022-06-17 出版日期:2024-02-20 发布日期:2024-02-20
  • 通讯作者: 强会英 E-mail:3466582439@qq.com;qhy2005ww@126.com
  • 作者简介:刘欢(1998—), 女, 硕士研究生, 研究方向为图论方向. E-mail: 3466582439@qq.com
  • 基金资助:
    国家自然科学基金资助项目(61962035)

2-distance sum distinguishing coloring of trees

Huan LIU1(),Huiying QIANG1,*(),Hongshen WANG2,Yu BAI1   

  1. 1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
    2. College of Mechanical and Electrical Engineering, Lanzhou University of Technology, Lanzhou 730050, Gansu, China
  • Received:2022-06-17 Online:2024-02-20 Published:2024-02-20
  • Contact: Huiying QIANG E-mail:3466582439@qq.com;qhy2005ww@126.com

RichHTML

2

PDF (PC)

371

摘要：

根据树图的结构特点, 应用数学归纳法、组合分析法及组合零点定理, 研究了图G的2-距离和可区别边染色和全染色问题, 得到了树的2-距离和可区别边色数和全色数。

关键词: 树图, 2-距离和可区别边色数, 2-距离和可区别全色数

Abstract:

Based on the structural characteristics of the trees, the 2-distance sum distinguishing edge(total) coloring of trees are studied by using the mathematical induction, combination analytic method and Combinatorial Nullstellensatz, and the 2-distance sum distinguishing edge(total) chromatic numbers are obtained.

Key words: tree, 2-distance sum distinguishing edge chromatic number, 2-distance sum distinguishing total chromatic number

中图分类号: 

  • O157.5

图1

星图"

图2

n=5或n=8"

图3

树图"

图4

双星图"

图5

n=7"

1 FLANDRIN E , MARCZYK A , PRZYBYLO J , et al. Neighbor sum distinguishing index[J]. Graphs and Combinatorics, 2013, 29 (5): 1329- 1336.
doi: 10.1007/s00373-012-1191-x
2 PILSNIAK M , WONIAK M . On the total-neighbor-distinguishing index by sums[J]. Graphs and Combinatorics, 2015, 31 (3): 771- 782.
doi: 10.1007/s00373-013-1399-4
3 潘文华, 徐常青. 无K4-图子式的图的邻和可区别边染色[J]. 数学进展, 2017, 46 (6): 41- 49.
PAN Wenhua , XU Changqing . Neighbor sum distinguishing edge colorings of K4-minor free graphs[J]. Advances in Mathematics, 2017, 46 (6): 41- 49.
4 YU Xiaowei , WANG Guanghui , WU Jianliang , et al. Neighbor sum distinguishing edge coloring of subcubic graphs[J]. Acta Mathematica Sinica, English Series, 2017, 33 (2): 252- 262.
doi: 10.1007/s10114-017-5516-9
5 田双亮, 杨环, 杨青, 等. 路的联的邻和可区别边染色[J]. 山东大学学报(理学版), 2020, 55 (9): 29- 35.
TIAN Shuangliang , YANG Huan , YANG Qing , et al. Neighbor sum distinguishing edge coloring of the join of paths[J]. Journal of Shandong University(Natural Science), 2020, 55 (9): 29- 35.
6 YAO Jingjing , YU Xiaowei , WANG Guanghui , et al. Neighbor sum distinguishing total coloring of 2-degenerate graphs[J]. Journal of Combinatorial Optimization, 2016, 34 (1): 1- 7.
7 强会英, 姚丽. 无K4-子式图的2-距离和可区别边染色[J]. 山东大学学报(理学版), 2021, 56 (11): 83- 86.
QIANG Huiying , YAO Li . 2-distance sum distinguishing edge coloring of K4-minor-free graphs[J]. Journal of Shandong University(Natural Science), 2021, 56 (11): 83- 86.
8 李泽鹏, 耿培伦, 陈祥恩. 树的D(r)-点可区别边染色[J]. 广州大学学报(自然科学版), 2020, 19 (1): 1- 7.
LI Zepeng , GENG Peilun , CHEN Xiang'en . D(r)-vertex distinguishing edge coloring of trees[J]. Journal of Guangzhou University(Natural Science Edition), 2020, 19 (1): 1- 7.
9 SONG Hongjie , XU Changqing . Neighbor sum distinguishing total chromatic number of K4-minor free graph[J]. Frontiers of Mathematics in China, 2017, 12 (4): 937- 947.
doi: 10.1007/s11464-017-0649-9
10 ZHANG Zhongfu , LIU Linzhong , WANG Jianfang . Adjacent strong edge coloring of graphs[J]. Applied Mathematics Letters, 2002, 15 (5): 623- 626.
doi: 10.1016/S0893-9659(02)80015-5
11 谭钧铭, 强会英, 王洪申. 单圈图的邻和可区别边染色[J]. 山东大学学报(理学版), 2022, 57 (2): 78- 83.
TAN Junming , QIANG Huiying , WANG Hongshen . Neighbor sum distinguishing edge coloring of unicyclic graphs[J]. Journal of Shandong University(Natural Science), 2022, 57 (2): 78- 83.
12 CHENG Xiaohan , DING Laihao , WANG Guanghui , et al. Improved bounds for neighbor sum (set) distinguishing choosability of planar graphs[J]. Discrete Mathematics, 2020, 343 (7): 111856.
doi: 10.1016/j.disc.2020.111856
[1] 孙晓玲,高玉斌,杜建伟,任建斌. 准树图的零阶广义Randic指数[J]. 《山东大学学报(理学版)》, 2022, 57(12): 96-102.
[2] 强会英,姚丽. 无K4-子式图的2-距离和可区别边染色[J]. 《山东大学学报(理学版)》, 2021, 56(11): 83-86.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] 王刚,许信顺*. 一种新的基于多示例学习的场景分类方法[J]. J4, 2010, 45(7): 108 -113 .
[2] 陆玮洁,主沉浮,宋 翠,杨艳丽 . 中药郁金中无机离子的毛细管电泳法测定[J]. J4, 2007, 42(7): 13 -18 .
[3] 赵君1,赵晶2,樊廷俊1*,袁文鹏1,3,张铮1,丛日山1. 水溶性海星皂苷的分离纯化及其抗肿瘤活性研究[J]. J4, 2013, 48(1): 30 -35 .
[4] 杨永伟1,2,贺鹏飞2,李毅君2,3. BL-代数的严格滤子[J]. 山东大学学报（理学版）, 2014, 49(03): 63 -67 .
[5] 韩亚飞,伊文慧,王文波,王延平,王华田*. 基于高通量测序技术的连作杨树人工林土壤细菌多样性研究[J]. 山东大学学报（理学版）, 2014, 49(05): 1 -6 .
[6] 孙小婷1,靳岚2*. DOSY在寡糖混合物分析中的应用[J]. J4, 2013, 48(1): 43 -45 .
[7] 任敏1,2,张光辉1. 右半直线上依分布收敛独立随机环境中随机游动的吸收概率[J]. J4, 2013, 48(1): 93 -99 .
[8] 徐俊峰. 关于复代数微分方程亚纯解的增长级[J]. J4, 2010, 45(6): 91 -93 .
[9] 解树涛,宋晓妍,石梅,陈秀兰,孙彩云,张玉忠* . 康宁木霉（Trichoderma koningii）SMF2分泌的peptaibols类抗菌肽Trichokonins抑菌活性研究[J]. J4, 2006, 41(6): 140 -144 .
[10] 刘保仓,史开泉 . S-粗集的信度特征[J]. J4, 2006, 41(5): 26 -29 .
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发