JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (2): 47-52, 58.doi: 10.6040/j.issn.1671-9352.0.2022.347

•   • Previous Articles     Next Articles

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

0

PDF (PC)

108

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

CLC Number: 

  • O157.5

Fig.1

Star Graph"

Fig.2

n=5 or n=8"

Fig.3

Tree"

Fig.4

Double-star graph"

Fig.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] Wenxin ZHANG,Qiang LI,Ning WANG,Xiaoli FAN,Hui WANG,Chengping JIANG,Yu LIANG. Differences in height, diameter at breast height, and growth relationships between them of common tree species at different altitudes in Shandong Province [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(1): 132-138.
[2] LIANG Yun, MEN Chang-qian, WANG Wen-jian. AdaBoost algorithm based on model decision tree [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(1): 67-75.
[3] QIAN Jin, TANG Da-wei, HONG Cheng-xin. Research on multi-granularity hierarchical sequential three-way decision model [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(9): 33-45.
[4] SUN Xiao-ling, GAO Yu-bin, DU Jian-wei, REN Jian-bin. Zeroth-order general Randic index of quasi-tree graphs [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(12): 96-102.
[5] WANG Jun-zhen, ZHANG Shu-min, GE Hui-fen. Generalized 3-connectivity of folded hypercubes [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(11): 42-49.
[6] LAI Jin-hua, LIU Meng-meng. On minimum Steiner k-Wiener index of trees with perfect matching [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(10): 66-71.
[7] CAO Run-feng, LIU Rui-xian, LIU Jing. Reliability analysis of road transportation system of hazardous chemicals tank truck based on fault tree and Bayesian network [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(1): 20-29.
[8] LYU Ning. Dynamics of the stage-structured population system with two kinds of pulses [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(12): 100-110.
[9] MA Hai-feng, YANG Jia-hai, XUE Qing-shui, JU Xing-zhong, ZHU Hao-zhi, LIN Tao, YUAN Xin-xin. A not-same frequency remote data possession checking method [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(5): 81-87.
[10] HE Xiao-li, SHE Yan-hong. Approximate concept and rule acquisition based on attribute granularity [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(5): 13-21.
[11] Chun-hui LING,Ming-zhong ZHANG,Gui-yun LYU,Hao-ran CUI,Pan YAP,Ye WEI,Sheng-yuan LIU,Feng-yun MA,Hua-tian WANG,Xiu-mei LIU,Ling MA. Application impacts analysis on natural forestry management for pine plantation in central and southern mountainous area of Shandong province [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(11): 8-17.
[12] WANG Qian. The contractible edges of a spanning tree and a perfect matching in k-connected graphs [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(8): 29-34.
[13] YANG Zhen-ya, TAI Xiu-guo, CAO Zhen-yu, LI Bo, CAO Bang-hua, WANG Shu-mei, WANG Xuan. A preliminary study on cold resistance of four introduced oaks seedlings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(5): 43-47.
[14] MA Li-fei, MO Qian, DU Hui. Research on classification for Chinese short film reviews [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(1): 52-57.
[15] TAN Hong-ye, ZHAO Jian, CHEN Qian. Finding potential errors in Chinese treebank based on inconsistencies [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(01): 26-30.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] WANG Gang, XU Xin-shun*. A new Multi-instance learning method for scene classification[J]. J4, 2010, 45(7): 108 -113 .
[2] LU Wei-jie,ZHU Chen-fu,SONG Cui and YANG Yan-li . Determination of inorganic cations in the Chinese traditional drug Yujin by capillary electrophoresis[J]. J4, 2007, 42(7): 13 -18 .
[3] ZHAO Jun1, ZHAO Jing2, FAN Ting-jun1*, YUAN Wen-peng1,3, ZHANG Zheng1, CONG Ri-shan1. Purification and anti-tumor activity examination of water-soluble asterosaponin from Asterias rollestoni Bell[J]. J4, 2013, 48(1): 30 -35 .
[4] YANG Yong-wei1, 2, HE Peng-fei2, LI Yi-jun2,3. On strict filters of BL-algebras#br#[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 63 -67 .
[5] HAN Ya-fei, YI Wen-hui, WANG Wen-bo, WANG Yan-ping, WANG Hua-tian*. Soil bacteria diversity in continuous cropping poplar plantation#br# by high throughput sequencing[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(05): 1 -6 .
[6] SUN Xiao-ting1, JIN Lan2*. Application of DOSY in oligosaccharide mixture analysis[J]. J4, 2013, 48(1): 43 -45 .
[7] REN Min1,2, ZHANG Guang-hui1. Absorbing probabilities of random walks in an independent random  environment convergence in distribution on the half-line[J]. J4, 2013, 48(1): 93 -99 .
[8] XU Jun-feng. On the growth of the meromorphic solutions of complex algebraic differential equations[J]. J4, 2010, 45(6): 91 -93 .
[9] XIE Shu-tao,SONG Xiao-yanAntimicrobial activities of Trichokonins: Peptaibollike antimicrobial peptides produced by Trichoderma koningii[J]. J4, 2006, 41(6): 140 -144 .
[10] LIU Bao-cang,SHI Kai-quan . Reliablity characteristics of Srough sets[J]. J4, 2006, 41(5): 26 -29 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd