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

作　　者：俞德龙 赵建宇 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135-152,共18页Pure Mathematics

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。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.

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

分 类 号：O17[理学—数学]