JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (12): 161-166.doi: 10.6040/j.issn.1671-9352.0.2023.385

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Neighbor sum distinguishing edge coloring of join graphs Cm∨Cn

BAI Yu, QIANG Huiying*, HE Jing   

  1. School of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2025-12-10

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Abstract: The neighbor sum distinguishing k-edge coloring of graph G is the coloring of a proper edge coloring of graph G, where the chromatic sum of adjacent vertex associated edge are not equal. The minimum number of colors k used for coloring is called the neighbor sum distinguishing edge chromatic numbers of graph G. This paper studies the neighbor sum distinguishing edge coloring problem of the join graph Cm∨Cn, obtaining the neighbor sum distinguishing edgechromatic numbers of the join graph Cm∨Cn(n≠m) and the upper bounds of Cn∨Cn, and extending this result to join graphs of general graphs.

Key words: cycle, join graphs, neighbor sum distinguishing edge coloring, neighbor sum distinguishing edge chromatic number

CLC Number: 

  • O157
[1] ZHANG Zhongfu, LIU Linzhong, WANG Jianfang. Adjacent strong edge coloring of graphs[J]. Applied Mathematics Letters, 2002, 15(5):623-626.
[2] FLANDRIN E, MARCZYK A, PRZYBYLO J, et al. Neighbor sum distinguishing index[J]. Graphs and Combinatorics, 2013, 29(5):1329-1336.
[3] 高荣双. 图的邻和可区别边染色和邻和可区别全染色[D]. 徐州:中国矿业大学,2017. GAO Rongshuang. Neighbor sum distinguishing edge colorings and total colorings of graphs[D]. Xuzhou: China University of Mining and Technology, 2017.
[4] 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.
[5] 姚丽,强会英,杨笑蕊. 两类笛卡尔积图的邻和可区别全染色[J]. 兰州交通大学学报,2020,39(3):125-129. YAO Li, QIANG Huiying, YANG Xiaorui. The neighbor sum distinguishing total coloring of two types cartesian graph[J]. Journal of Lanzhou Jiaotong University, 2020, 39(3):125-129.
[6] 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.
[7] 谭钧铭,强会英,刘欢,等.双圈图的邻和可区别边染色[J]. 西南大学学报(自然科学版),2022,44(6):1-8. TAN Junming, QIANG Huiying, LIU huan, et al. Neighbor sum distinguishing edge coloring of bicyclic graphs[J]. Journal of Southwest University(Natural Science), 2022, 44(6):1-8.
[8] 刘欢,强会英,王洪申. 单圈图的D(2)-点和可区别边染色[J]. 南开大学学报(自然科学版),2024(1):91-97. LIU huan, QIANG Huiying, WANG Hongshen. D(2)-Vertex sum distinguishing edge coloring of unicyclic graphs[J]. Journal of Nankai University(Natural Science), 2024(1):91-97.
[9] 姚京京,邵泽玲,徐常青. Δ=3的图的邻和可区别全可选性(英文)[J]. 数学进展,2016,45(3):343-348. YAO Jingjing, SHAO Zeling, XU Changqing. Neighbor sum distinguishing total choosability of graphs with Δ=3[J]. Advances in Mathematics, 2016, 45(3):343-348.
[10] 王芹,杨超,殷志祥,等. 三类联图的2-距离和可区别边染色[J]. 华中师范大学学报(自然科学版),2024,58(2):178-183. WANG Qin, YANG Chao, YIN Zhixiang, et al. 2-distance sum distinguishing edge colorings of three types of join graphs[J]. Journal of Central China Normal University(Natural Sciences), 2024, 58(2):178-183.
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[5] WANG Bing . Properties of a quasi-claw-free graph[J]. J4, 2007, 42(10): 111 -113 .
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