JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (12): 134-139.doi: 10.6040/j.issn.1671-9352.0.2022.276

•   • Previous Articles     Next Articles

Adjacent vertex distinguishing edge coloring of IC-planar graphs without intersecting triangles

Jin LI(),Changqing XU*()   

  1. School of Science, Hebei University of Technology, Tianjin 300401, China
  • Received:2022-05-02 Online:2023-12-20 Published:2023-12-19
  • Contact: Changqing XU E-mail:lj13663389266@163.com;chqxu@hebut.edu.cn

RichHTML

0

PDF (PC)

190

Abstract:

Let φ be an l-proper edge coloring of graph G and Cφ(u) be the color set of all edges incident with vertex u of G. An l-adjacent vertex distinguishing edge coloring of a graph G is the coloring φ such that Cφ(u) and Cφ(v) are distinct for any edge uv of G, denoted by an l-avd coloring. The minimum positive integer l for an l-avd coloring of G is the adjacent vertex distinguishing edge chromatic number, denoted by χ′a(G). In this paper, we study the adjacent vertex distinguishing edge coloring of an IC-normal planar graph G without intersecting triangles by using the discharging method and get that χ′a(G)≤max{Δ(G)+2, 12}.

Key words: adjacent vertex distinguishing edge coloring, discharging method, IC-normal planar graph

CLC Number: 

  • O157.5

Table 1

Relation between dG(u) and dT(u)"

条件 dT(u)
3≤dG(u)≤6 dT(u)=dG(u)
dG(u)=7 dT(u)≥6
dG(u)=8 dT(u)≥6
dG(u)=9 dT(u)≥7
dG(u)≥10 dT(u)≥6
1 BONDY J A , MURTY U S R . Graph theory with applications[M]. New York: North-Holland, 2008.
2 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
3 HORŇÁK M , HUANG Danjun , WANG Weifan . On neighbor-distinguishing index of planar graphs[J]. Journal of Graph Theory, 2014, 76 (4): 262- 278.
doi: 10.1002/jgt.21764
4 BONAMY M, BOUSQUET N, HOCQUARD H. Adjacent vertex-distinguishing edge coloring of graphs[C]//The Seventh European Conference on Combinatorics, Graph Theory and Applications, 2013, 16: 313-318.
5 严丞超, 黄丹君, 王维凡. 围长至少为4的可平面图的邻点可区别边染色[J]. 数学研究, 2012, 45 (4): 331- 341.
YAN Chengchao , HUANG Danjun , WANG Weifan . Adjacent vertex distinguishing edge-colorings of planar graphs with girth at least four[J]. Journal of Mathematical Study, 2012, 45 (4): 331- 341.
6 HUANG Danjun , MIAO Zhengke , WANG Weifan . Adjacent vertex distinguishing indices of planar graphs without 3-cycles[J]. Discrete Mathematics, 2015, 338 (3): 139- 148.
doi: 10.1016/j.disc.2014.10.010
7 HUANG Danjun , ZHANG Xiaoxiu , WANG Weifan , et al. Adjacent vertex distinguishing edge coloring of planar graphs without 3-cycles[J]. Discrete Mathematics, Algorithms and Applications, 2020, 12 (4): 2050035.
doi: 10.1142/S1793830920500354
8 刘卓雅, 徐常青. 无相交三角形平面图的邻点可区别边染色[J]. 山东大学学报(理学版), 2020, 55 (9): 36- 41.
LIU Zhuoya , XU Changqing . Adjacent vertex distinguishing edge coloring of planar graphs without intersecting triangles[J]. Journal of Shandong University (Natural Science), 2020, 55 (9): 36- 41.
9 LIU Zhuoya , XU Changqing . Adjacent vertex distinguishing edge coloring of IC-planar graphs[J]. Journal of Combinatorial Optimization, 2022, 43 (4): 710- 726.
doi: 10.1007/s10878-021-00807-0
10 宋超, 徐常青. 不含三角形的IC-可平面图的邻点可区别边染色[J]. 数学进展, 2022, 51 (5): 817- 822.
SONG Chao , XU Changqing . Adjacent vertex distinguishing edge colorings of triangle free IC-planar graphs[J]. Advances in Mathematics (China), 2022, 51 (5): 817- 822.
[1] LIU Zhuo-ya, XU Chang-qing. Adjacent vertex distinguishing edge coloring of planar graphs without intersecting triangles [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(9): 36-41.
[2] SUN Lin, CAI Hua. On the vertex-arboricity of embedded graphs [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(02): 38-42.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] YANG Jun. Characterization and structural control of metalbased nanomaterials[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2013, 48(1): 1 -22 .
[2] HE Hai-lun， CHEN Xiu-lan* . Circular dichroism detection of the effects of denaturants and buffers on the conformation of cold-adapted protease MCP-01 and  mesophilic protease BP01[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2013, 48(1): 23 -29 .
[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] SUN Xiao-ting1, JIN Lan2*. Application of DOSY in oligosaccharide mixture analysis[J]. J4, 2013, 48(1): 43 -45 .
[5] LUO Si-te, LU Li-qian, CUI Ruo-fei, ZHOU Wei-wei, LI Zeng-yong*. Monte-Carlo simulation of photons transmission at alcohol wavelength in  skin tissue and design of fiber optic probe[J]. J4, 2013, 48(1): 46 -50 .
[6] YANG Lun, XU Zheng-gang, WANG Hui*, CHEN Qi-mei, CHEN Wei, HU Yan-xia, SHI Yuan, ZHU Hong-lei, ZENG Yong-qing*. Silence of PID1 gene expression using RNA interference in C2C12 cell line[J]. J4, 2013, 48(1): 36 -42 .
[7] MAO Ai-qin1,2, YANG Ming-jun2, 3, YU Hai-yun2, ZHANG Pin1, PAN Ren-ming1*. Study on thermal decomposition mechanism of  pentafluoroethane fire extinguishing agent[J]. J4, 2013, 48(1): 51 -55 .
[8] YANG Ying, JIANG Long*, SUO Xin-li. Choquet integral representation of premium functional and related properties on capacity space[J]. J4, 2013, 48(1): 78 -82 .
[9] LI Yong-ming1, DING Li-wang2. The r-th moment consistency of estimators for a semi-parametric regression model for positively associated errors[J]. J4, 2013, 48(1): 83 -88 .
[10] DONG Wei-wei. A new method of DEA efficiency ranking for decision making units with independent subsystems[J]. J4, 2013, 48(1): 89 -92 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd