Zhang, Heping; Zhao, Shuang; Lin, Ruizhi The forcing polynomial of catacondensed hexagonal systems. (English) Zbl 1462.05190 MATCH Commun. Math. Comput. Chem. 73, No. 2, 473-490 (2015). Summary: D. J. Klein and M. Randić [“Innate degree of freedom of a graph”, J. Comput. Chem. 8, 516–521 (1987; doi:10.1002/jcc.540080432)] defined the innate degree of freedom of a graph \(G\) as the sum of the forcing numbers (innate degree of freedom) of perfect matchings of graph \(G\). In this paper, we propose the forcing polynomial of a graph as a counting polynomial for perfect matchings with the same forcing number, from which the perfect matching count and innate degree of freedom of the graph can be easily obtained. We give recursive expressions for the forcing polynomial of hexagonal chains, and general catacondensed hexagonal systems as well. In particular, explicit expressions of the forcing polynomial and asymptotic behavior of the innate degree of freedom for zigzag hexagonal chains are obtained. Cited in 10 Documents MSC: 05C31 Graph polynomials Keywords:forcing polynomial of hexagonal chains; zigzag hexagonal chains PDFBibTeX XMLCite \textit{H. Zhang} et al., MATCH Commun. Math. Comput. Chem. 73, No. 2, 473--490 (2015; Zbl 1462.05190)