线性亚苯基系统的强迫和反强迫多项式

Forcing and anti-forcing polynomials of linear phenylene systems

图G的一个完美匹配M的强迫数是M中的最少边数,满足这些边不被G中其它的完美匹配所包含.M的反强迫数是从G中删去M之外的边,使得M是删边之后的图中唯一的完美匹配所需删去的最少边数.图的强迫和反强迫多项式是最近提出的分别反映图中所有完美匹配强迫数和反强迫数分布的计数多项式.文中计算了线性亚苯基系统的强迫和反强迫多项式,得到了它们精确的表达式,并揭示了线性亚苯基系统的自由度和反自由度的渐近行为.

The forcing number of a perfect matching M of a graph G is the minimum number of edges in M such that these edges are not contained in other perfect matchings of G.The anti-forcing number of M is the minimum number of edges of G not in M such that M is the unique perfect matching of the subgraph obtained by deleting these edges from G.Recently,the forcing and antiforcing polynomials of a graph G were proposed respectively as counting polynomials for describing the distributions of forcing and anti-forcing numbers of all perfect matchings of G.In this paper,the forcing and anti-forcing polynomials of linear phenylene systems are computed,and their explicit expressions are obtained.As corollaries,the asymptotic behaviors of degree of freedom and degree of anti-freedom of linear phenylene systems are revealed respectively.