六个苯环生成的六角系统的自由度

The Degrees of Freedom of a Hexagonal Systems Generated by Six Benzene Rings

设 M 是图 G 的一个完美匹配,S 是 M 的一个子集。 若 S 不被 G 中其它完美匹配所包含,则称 S 是 M 的一个强迫集。 包含边数最少的强迫集的势称为 M 的强迫数,图 G 中所有完美匹配的强 迫数的和称作图 G 的自由度。 图的强迫多项式是最近提出的刻画全体强迫数分布的一种计数多项 式。 在本文中,利用强迫多项式,计算了所有由六个苯环生成的六角系统的自由度,井对比了它 们的平均自由度。

Let M be a perfect matching of a graph G, and S be a subset of M . S is called a forcing set of M if S is not contained in other perfect matchings of G. The cardinality of a forcing set with the least number of edges is defined as the forcing number of M . The sum of forcing numbers of all perfect matchings of G is called the degree of freedom of G. The forcing polynomial of a graph is a recently proposed counting polynomial that characterizes the distribution of all forcing numbers. In this paper, the degrees of freedom of all hexagonal systems generated by six benzene rings were calculated using forcing polynomials, and their average degrees of freedom were compared.