Forcing and anti-forcing polynomials of perfect matchings of a pyrene system
Abstract
The forcing number of a perfect matching of a graph was introduced by Harary et al., which originated from Klein and Randi\'{c}'s ideal of innate degree of freedom of Kekul\'{e} structure in molecular graph. On the opposite side in some sense, Vuki\v{c}evi\'{c} and Trinajsti\'{e} proposed the anti-forcing number of a graph, afterwards Lei et al. generalized this idea to single perfect matching. Recently the forcing and anti-forcing polynomials of perfect matchings of a graph were proposed as counting polynomials for perfect matchings with the same forcing number and anti-forcing number respectively. In this paper, we obtain the explicit expressions of forcing and anti-forcing polynomials of a pyrene system. As consequences, the forcing and anti-forcing spectra of a pyrene system are determined.
Keywords
Cite
@article{arxiv.2004.05112,
title = {Forcing and anti-forcing polynomials of perfect matchings of a pyrene system},
author = {Kai Deng and Saihua Liu and Xiangqian Zhou},
journal= {arXiv preprint arXiv:2004.05112},
year = {2020}
}