Forcing and anti-forcing polynomials of a polyomino graph
Abstract
The forcing number of a perfect matching in a graph is the smallest number of edges inside that can not be contained in other perfect matchings. The anti-forcing number of is the smallest number of edges outside whose removal results in a subgraph with a single perfect matching, that is . 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.
Cite
@article{arxiv.2012.12898,
title = {Forcing and anti-forcing polynomials of a polyomino graph},
author = {Kai Deng and Huazhong Lü and Tingzeng Wu},
journal= {arXiv preprint arXiv:2012.12898},
year = {2020}
}