JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (11): 83-86.doi: 10.6040/j.issn.1671-9352.0.2020.198

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2-distance sum distinguishing edge coloring of K4-minor-free graphs

QIANG Hui-ying, YAO Li*   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2021-11-15

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Abstract: Let φ be a proper edge coloring of graph G, for any u,v∈V(G), if dG(u,v)≤2 such that f(u)≠f(v) where f(u)=∑uw∈E(G)φ(uw), then φ is the 2-distance sum distinguishing edge coloring of graph G. The 2-distance sum distinguishing edge coloring of K4-minor-free graphs are studied by using the methods of contradiction and constructing coloring function, and a upper bound of the 2-distance sum distinguishing edge chromatic number of K4-minor-free graphs is obtained.

Key words: 2-distance sum distinguishing edge coloring, 2-distance sum distinguishing edge chromatic, K4-minor-free graphs

CLC Number: 

  • O157.5
[1] ZHANG Z F, LIU L Z, WANG J F. Adjacent strong edge coloring of graphs[J]. Applied Mathematics Letters, 2002, 15(5):623-626.
[2] 王维凡, 王平. 没有K4-图子式的图的邻点可区别全染色[J]. 中国科学(A辑: 数学), 2009, 39(12):1462-1472. WANG Weifan, WANG Ping. Neighbor vertex distinguishing total coloring of graphs[J]. Science in China(Series A: Mathematics), 2009, 39(12):1462-1472.
[3] 史小艺,张宁,万慧敏. K4-minor-free图的邻点可区别全染色[J]. 五邑大学学报,2012,26(4):9-13. SHI Xiaoyi, ZHANG Ning, WAN Huimin. K4-minor-free neighbor vertex distinguishing total coloring of graphs[J]. Journal of Wuyi University(Natural Science Edition), 2012, 26(4):9-13.
[4] WANG W F, WANG Y Q. Adjacent vertex-distinguishing edge colorings of K4-minor free graphs[J]. Applied Mathematics Letters, 2011, 24(12):2034-2037.
[5] FLANDRIN E, MARCZYK A, PRZYBYŁO J, et al. Neighbor sum distinguishing index[J]. Graphs and Combinatorics, 2013, 29(5):1329-1336.
[6] WANG G H, YAN G Y. An improved upper bound for the neighbor sum distinguishing index of graphs[J]. Discrete Applied Mathematics, 2014, 175:126-128.
[7] DONG A J, WANG G H, ZHANG J H. Neighbor sum distinguishing edge colorings of graphs with bounded maximum average degree[J]. Discrete Applied Mathematics, 2014, 166: 84-90.
[8] DONG A J, WANG G H. Neighbor sum distinguishing total colorings of graphs with bounded maximum average degree[J]. Acta Mathematica Sinica, English Series, 2014, 30(4):703-709.
[9] LI H L, LIU B Q, WANG G H. Neighbor sum distinguishing total colorings of K4-minor free graphs[J]. Frontiers of Mathematics in China, 2013, 8(6):1351-1366.
[10] ZHANG J H, DING L H, WANG G H, et al. Neighbor sum distinguishing index of K4-minor free graphs[J]. Graphs and Combinatorics, 2016, 32(4):1621-1633.
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