Abstract
The forcing number of a perfect matching M of a graph G is the minimal number of edges of M that are contained in no other perfect matchings of G. The anti-forcing number of M in G is the minimal number of edges of G not in M whose deletion results in a subgraph with a unique perfect matching M. 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 focus on $$2\times n$$ and $$3\times {2n}$$ grids, and obtain the explicit expressions of their forcing and anti-forcing polynomials. As corollaries, their forcing and anti-forcing spectra are obtained.
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