Counting the maximal and perfect matchings in benzenoid chains

Lingjuan Shi and Kai Deng

Applied Mathematics and Computation, 2023, vol. 447, issue C

Abstract: Došlić et al. obtained general generating functions for the numbers of maximal matchings in three classes of benzenoid chains. By using the Hosoya vector and k-matching vector, Cruz et al. and Oz et al. researched the Hosoya index and the k-matching number of benzenoids, respectively. Inspired by these results, by using the maximal matching vector, we show that the number of maximal matchings of a benzenoid chain with n hexagons equals to the product of n certain matrices. In addition, we obtain the numbers of perfect matchings of all benzenoid chains.

Keywords: Maximal matching; Perfect matching; Benzenoid chain (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:447:y:2023:i:c:s0096300323000917

DOI: 10.1016/j.amc.2023.127922

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