Journal of Mathematical Chemistry

, Volume 57, Issue 1, pp 202–225 | Cite as

Forcing and anti-forcing polynomials of perfect matchings for some rectangle grids

  • Shuang Zhao
  • Heping ZhangEmail author
Original Paper


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.


Grid graph Dimer covering Perfect matching Forcing polynomial Anti-forcing polynomial 


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsLanzhou UniversityLanzhouPeople’s Republic of China

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