苯环数目不超过六的六角系统的双强迫多项式
Di-Forcing Polynomials of Hexagonal System in Which the Number of Benzene Rings Does Not Exceed Six
摘要: 六角系统是一个2-连通的有限平面二部图，其中每个内面边界都是单位的正六边形。具有凯库勒结构的六角系统H的双强迫多项式是H的所有完美匹配的强迫数和反强迫数的二元计数多项式。本文计算了苯环数目不超过六的六角系统的双强迫多项式，由此得到其强迫多项式，反强迫多项式，内自由度与外自由度，为六角系统的结构分析提供了新的数学工具和结果。
Abstract: The hexagonal system is a 2-connected finite plane bipartite graph, in which each inner boundary is a regular hexagon of a unit. The di-forcing polynomials of hexagonal systems H with Kekulé structure are the binary counting polynomials of all perfect matchings forcing and anti-forcing numbers of H. In this paper, the di-forcing polynomials of hexagonal systems with no more than six benzene rings are calculated, from which the forcing polynomials, anti-forcing polynomials, internal and external degrees of freedom are obtained, it provides a new mathematical tool and results for the structural analysis of hexagonal system.
文章引用：俞德龙, 赵建宇, 张诗晗. 苯环数目不超过六的六角系统的双强迫多项式[J]. 理论数学, 2024, 14(8): 135-152. https://doi.org/10.12677/pm.2024.148312

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