“X”型梯状图和“T”型梯状图的反强迫多项式
The Anti-Forcing Polynomials of “X” Type and “T” Type Ladderlike Graphs
DOI: 10.12677/AAM.2020.99166, PDF,    国家自然科学基金支持
作者: 王倩倩, 姚海元*:西北师范大学数学与统计学院,甘肃 兰州;韩振云:临夏市第五中学,甘肃 临夏
关键词: 完美匹配梯状图反强迫多项式部分反强迫多项式Perfect Matching Ladderlike Graph Anti-Forcing Polynomial Partial Anti-Forcing Polynomial
摘要: 通过某个顶点关联边的匹配情况分类计算梯子图的部分反强迫多项式,进而根据对完美匹配进行分类和图的分解,得到了“X”型梯状图和“T”型梯状图的反强迫多项式。
Abstract: The partial anti-forcing polynomials are calculated by the matching classification of a vertex associated edge in a ladder graph, and then the anti-force polynomials of the “X” type and the “T” type ladderlike graphs are obtained.
文章引用:王倩倩, 韩振云, 姚海元. “X”型梯状图和“T”型梯状图的反强迫多项式[J]. 应用数学进展, 2020, 9(9): 1404-1416. https://doi.org/10.12677/AAM.2020.99166

参考文献

[1] Li, X.L. (1997) Hexagonal Systems with Forcing Single Edges. Discrete Applied Mathematics, 72, 295-301. [Google Scholar] [CrossRef
[2] Vukiěević, D. and Trinajstić, N. (2007) On the Anti-Forcing Number of Benzenoids. Journal of Mathematical Chemistry, 42, 575-583. [Google Scholar] [CrossRef
[3] Vukiěević, D. and Trinajstić, N. (2008) On the Anti-Kekule Number and Anti-Forcing Number of Cata-Condensed Benzenoids. Journal of Mathematical Chemistry, 43, 719-726. [Google Scholar] [CrossRef
[4] Lei, H.C., Yeh, Y.N. and Zhang, H.P. (2016) Anti-Forcing Numbers of Perfect Matchings of Graphs. Discrete Applied Mathematics, 202, 95-105. [Google Scholar] [CrossRef
[5] Deng, H.Y. (2008) The Anti-Forcing Number of Hexagonal Chains. MATCH Communications in Mathematical and in Computer Chemistry, 60, 58675-58682.
[6] Deng, H.Y. (2008) The Anti-Forcing Number of Double Hexagonal Chains. MATCH Communications in Mathematical and in Computer Chemistry, 60, 183-192.
[7] Zhang, Q., Bian, H. and Vumar, E. (2011) On the Anti-Kekule Number and Anti-Forcing Number of Cata Condensed Phenylenes. MATCH Communications in Mathematical and in Computer Chemistry, 65, 799-806.
[8] 蒋晓艳, 程晓胜. 硼氮富勒烯图的反强迫数[J]. 湖南师范学院学报(自然科学版), 2013, 33(3): 28-30.
[9] Zhang, F.J. and Liu, Y.T. (1993) Estimation of the Resonance Energy of Benzenoid Hydrocarbon. Chinese Science Bulletin, 38, 2040-2043.
[10] Klein, D.J. and Rosenfeld, V. (2014) Forcing, Freedom, & Uniqueness in Graph Theory & Chemistry. Croatica Chemica Acta, 87, 49-59. [Google Scholar] [CrossRef
[11] Deng, K. and Zhang, H.P. (2017) Anti-Forcing Spectrum of Any Cata-Condensed Hexagonal System Is Continuous. Frontiers of Mathematics in China, 12, 325-337. [Google Scholar] [CrossRef
[12] Deng, K. and Zhang, H.P. (2015) Anti-Forcing Spectrum of Perfect Matchings of Graphs. Journal of Combinatorial Optimization, 33, 660-680. [Google Scholar] [CrossRef
[13] Shi, L.J. and Zhang, H.P. (2016) Forcing and Anti-Forcing Numbers of (3,6)-Fullerences. MATCH Communications in Mathematical and in Computer Chemistry, 76, 597-614.
[14] Hwang, H.-K., Lei, H.C., Yeh, Y.-N. and Zhang, H.P. (2015) Distribution of Forcing and Anti-Forcing Numbers of Random Perfect Matchings on Hexagonal Chains and Crowns. http://140.109.74.92/hk/?p=873
[15] Zhao, S. and Zhang, H.P. (2019) Forcing and Anti-Forcing Polynomials of Perfect Matchings for Some Rectangle Grids. Journal of Mathematical Chemistry, 57, 202-225. [Google Scholar] [CrossRef
[16] 赵爽. 关于一些图类的强迫和反强迫多项式的研究[D]: [博士学位论文]. 兰州: 兰州大学, 2018.
[17] 韩振云, 王杰彬. 梯子图的完美匹配的反强迫谱与斐波那契数列[J]. 兰州工业学院学报, 2020, 27(1): 85-90.
[18] 姚海元, 王杰彬, 王旭. 循环梯状图的完美匹配的反强迫谱与卢卡斯数[J]. 西北师范大学学报(自然科学版), 2018, 54(2): 21-25.
[19] 韩振云, 姚海元. 删边梯子图和“L”型梯子图的反强迫数[J]. 应用数学进展, 2019, 8(8): 1352-1361.
[20] Koshy, T. (2001) Fibonacci and Lucas Numbers with Applications. Wiley, New York.
[21] 邵嘉裕. 组合数学[M]. 上海: 同济大学出版社, 1988: 22.
[22] Sloane, N.J.A. (2020) The On-Line Encyclopedia of Integer Sequences. http://oeis.org/