螺旋六角para-链的最大匹配的强迫数
The Forcing Number of Maximum Matching in Spiro Hexagonal Para-Chain
DOI: 10.12677/AAM.2020.92029, PDF,    国家自然科学基金支持
作者: 李晶晶, 边 红：新疆师范大学数学科学学院，新疆 乌鲁木齐；于海征：新疆大学数学与系统科学学院，新疆 乌鲁木齐
关键词: 最大匹配；强迫集；强迫数；螺旋六角para-链；Maximum Matching； Forcing Set； Forcing Number； Spiro Hexagonal Para-Chain
摘要: 令M是图G的一个最大匹配，S是M的一个子集。如果S除了被M包含而不被G的其它最大匹配所包含，那么称S是M的一个强迫集(forcing set)。M的最小强迫集所包含的边数称作是M的强迫数(forcing number)，记为fm(G, M)。图G的所有最大匹配的强迫数的最小值称为G的最小强迫数(Minimum forcing number)，记作fm(G)。在本文中，我们给出了螺旋六角para-链的最大匹配的强迫数的确切值。
Abstract: Let G be a graph with a maximum matching M. A subset S ⊆ M is called a forcing set of M if S is con-tained in only one maximum matching M of G. A forcing set of M with minimum cardinality is the minimum forcing set of M and its cardinality is called the forcing number of M, denoted by fm(G, M). The minimum forcing number of all maximum matchings in G is called the forcing number of G, denoted by fm(G). In this paper, we obtain the forcing number of maximum matching in spiro hex-agonal para-chain.
文章引用：李晶晶, 边红, 于海征. 螺旋六角para-链的最大匹配的强迫数[J]. 应用数学进展, 2020, 9(2): 251-256. https://doi.org/10.12677/AAM.2020.92029

参考文献

[1] Randić, M. and Klein, D.J. (1985) Kekulé Valence Structures Revisited, Innate Degrees of Freedom of π-Electron Couplings. In: Trinajstić N., Eds., Mathematical and Computational Concepts in Chemistry, Wiley, New York, 274-282.
[2] Harary, F., Klein, D.J. and Živković, T.P. (1991) Graphical Properties of Polyhexes: Perfect Matching Vector and Forcing. Journal of Mathematical Chemistry, 6, 295-306. [Google Scholar] [CrossRef] 
[3] Vukičević, D. and Sedlar, J. (2004) Total Forcing Number of the Tri-angular Grid. Mathematical Communications, 9, 169-179.
[4] Xu, S.-J., Zhang, H.-P. and Cai, J.-Z. (2015) Complete Forcing Numbers of Catacondensed Hexagonal Systems. Journal of Combinatorial Optimization, 29, 803-814. [Google Scholar] [CrossRef] 
[5] Lovász, L. and Plummer, M.D. (1986) Matching Theory. Akademiai Kiado, Amsterdam, North-Holland.
[6] Vukičević, D., Zhao, S., Sedlar, J., Xu, S.-J. and Došlić, T. (2018) Global Forcing Number for Maximal Matchings. Discrete Mathematics, 341, 801-809. [Google Scholar] [CrossRef] 
[7] Zhong, L. (2012) The Harmonic Index on Unicyclic Graphs. Ars Combinatoria, 104, 261-269.
[8] Yarahmadi, Z., Došlić, T. and Moadi, S. (2013) Chain Hexagonal Cacti: Extremal with Respect to the Eccentric Connectivity Index. Iranian Journal of Mathematical Chemistry, 4, 123-126.
[9] 王洪伟. 二部图的匹配强迫数[D]: [博士学位论文]. 兰州: 兰州大学, 2008.

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