不含4-圈的IC-平面图的严格邻点可区别边染色
Strict Neighbor-Distinguishing Edge-Coloring of IC-Planar Graphs without 4-Cycles
DOI: 10.12677/AAM.2025.144141, PDF,   
作者: 王加炎：浙江师范大学数学科学学院，浙江 金华
关键词: 严格邻点可区别边染色；IC-平面图；圈；Strict Neighbor-Distinguishing Edge-Coloring； IC-Planar Graph； Cycle
摘要: 图的严格邻点可区别边染色是指图中的任意一对相邻顶点的颜色集合互相不包含。 称使得图具有 严格邻点可区别边染色的最小正整数为图的严格邻点可区别边色数。 本文运用权转移方法证明： 对于不含4-圈的IC-平面图，其严格邻点可区别边色数为两倍最大度与13 的和。
Abstract: The strict neighbor-distinguishing edge coloring of a graph refers to an edge coloring where for any pair of adjacent vertices, their respective color sets neither contain nor are contained within each other. The smallest positive integer that enables a graph to admit such a coloring is called the strict neighbor-distinguishing edge chromatic number. In this paper, we employ the discharging method to prove that for IC-planar graphs without 4-cycles, the strictly adjacent vertex-distinguishing edge chromatic number equals the sum of twice the maximum degree and 13.
文章引用：王加炎. 不含4-圈的IC-平面图的严格邻点可区别边染色[J]. 应用数学进展, 2025, 14(4): 75-82. https://doi.org/10.12677/AAM.2025.144141

参考文献

[1] Zhang, Z., Liu, L. and Wang, J. (2002) Adjacent Strong Edge Coloring of Graphs. Applied Mathematics Letters, 15, 623-626.
https://doi.org/10.1016/s0893-9659(02)80015-5
[2] Akbari, S., Bidkhori, H. and Nosrati, N. (2006) R-Strong Edge Colorings of Graphs. Discrete Mathematics, 306, 3005-3010.
https://doi.org/10.1016/j.disc.2004.12.027
[3] Wang, Y., Wang, W. and Huo, J. (2015) Some Bounds on the Neighbor-Distinguishing Index of Graphs. Discrete Mathematics, 338, 2006-2013.
https://doi.org/10.1016/j.disc.2015.05.007
[4] Vuˇckovi´c, B. (2017) Edge-Partitions of Graphs and Their Neighbor-Distinguishing Index. Dis- crete Mathematics, 340, 3092-3096.
https://doi.org/10.1016/j.disc.2017.07.005
[5] Joret, G. and Lochet, W. (2020) Progress on the Adjacent Vertex Distinguishing Edge Coloring Conjecture. SIAM Journal on Discrete Mathematics, 34, 2221-2238.
https://doi.org/10.1137/18m1200427
[6] Huang, D., Cai, H., Wang, W. and Huo, J. (2023) Neighbor-Distinguishing Indices of Planar Graphs with Maximum Degree Ten. Discrete Applied Mathematics, 329, 49-60.
https://doi.org/10.1016/j.dam.2022.12.023
[7] Huo, J., Li, M. and Wang, Y. (2022) A Characterization for the Neighbor-Distinguishing Index of Planar Graphs. Symmetry, 14, Article 1289.
https://doi.org/10.3390/sym14071289
[8] Zhu, E., Wang, Z. and Zhang, Z. (2009) On the Smarandachely Adjacent Vertex Edge Coloring of Some Double Graphs. Journal of Shandong University (Natural Science), 44, 25-29.
[9] Gu, J., Wang, W., Wang, Y. and Wang, Y. (2020) Strict Neighbor-Distinguishing Index of Subcubic Graphs. Graphs and Combinatorics, 37, 355-368.
https://doi.org/10.1007/s00373-020-02246-w
[10] 刘信生, 刘旺发. 图的Smarandachely邻点无圈边色数的一个上界[J]. 系统科学与数学, 2013, 33(5): 550-554.
[11] Przyby-lo, J. and Kwa´sny, J. (2020) On the Inclusion Chromatic Index of a Graph. Journal of Graph Theory, 97, 5-20.
https://doi.org/10.1002/jgt.22636
[12] Wang, W., Jing, P., Gu, J. and Wang, Y. (2023) Local Neighbor-Distinguishing Index of Graphs. Bulletin of the Malaysian Mathematical Sciences Society, 46, Article No. 83.
https://doi.org/10.1007/s40840-023-01474-6
[13] 井普宁. 图的严格邻点可区别边染色及区间边染色[D]: [博士学位论文]. 金华: 浙江师范大学, 2023.

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