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

作　　者：赵建宇 俞德龙 张诗晗 

机构地区：[1]西北师范大学数学与统计学院,甘肃 兰州

出　　处：《理论数学》2024年第8期209-228,共20页Pure Mathematics

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。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.

关 键 词：完美匹配 六角系统 双强迫多项式 强迫多项式 反强迫多项式 区分 

分 类 号：O17[理学—数学]