七个苯环生成的六角系统的双强迫多项式
Double Forcing Polynomials of a Hexagonal System Generated by Seven Benzene Rings
摘要: 匹配是一个边的集合，其中任意两条边都没有公共顶点。对于图G的一个匹配M，如果M中的边能够将G的所有顶点两两配对，则称该匹配为完美匹配。七个苯环生成的六角系统中具有完美匹配的六角系统个数为190个。本文计算出了这190个七个苯环生成的六角系统的双强迫多项式。同时将双强迫多项式、强迫多项式、反强迫多项式、完美匹配个数、自由度与反自由度对于图的区分情况进行了统计与比较。
Abstract: A matching is a set of edges, where any two edges have no common vertices. For a match M in graph G, if the edges in M can pair all the vertices of G in pairs, the match is said to be a perfect match. The number of hexagonal systems with perfect matchings among the hexagonal systems generated by seven benzene rings is 190. This paper calculates the di-forcing polynomials of the hexagonal system generated by these 190 seven benzene rings. At the same time, the discrimination of di-forcing polynomials, forced polynomials, anti-forced polynomials, number of perfect matches, degrees of freedom and anti-degrees of freedom for graphs is statistically compared.
文章引用：赵建宇, 俞德龙, 张诗晗. 七个苯环生成的六角系统的双强迫多项式[J]. 理论数学, 2024, 14(8): 209-228. https://doi.org/10.12677/pm.2024.148319

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