论文标题
多粒图的强迫和抗强化多项式
Forcing and anti-forcing polynomials of a polyomino graph
论文作者
论文摘要
$ g $中完美匹配的$ m $的强迫数量是$ m $内部最小的边缘数量，这些边缘无法包含在其他完美匹配中。 $ m $的反施加数量是$ m $以外的最小边缘数量，其去除会导致单个完美匹配（即$ m $）的子图。最近，为了研究强迫数量和抗强迫数量的分布，分别提出了强迫多项式和抗强化多项式。在这项工作中，获得了多元图的强迫和抗强化多项式。结果，确定了该多元图的强迫和抗强化光谱，并且分别揭示了所有抗强迫数量的自由度和所有反强迫数量的总和的渐近行为。
The forcing number of a perfect matching $M$ in a graph $G$ is the smallest number of edges inside $M$ that can not be contained in other perfect matchings. The anti-forcing number of $M$ is the smallest number of edges outside $M$ whose removal results in a subgraph with a single perfect matching, that is $M$. Recently, in order to investigate the distributions of forcing numbers and anti-forcing numbers, the forcing polynomial and anti-forcing polynomial were proposed, respectively. In this work, the forcing and anti-forcing polynomials of a polyomino graph are obtained. As consequences, the forcing and anti-forcing spectra of this polyomino graph are determined, and the asymptotic behaviors on the degree of freedom and the sum of all anti-forcing numbers are revealed, respectively.
