Enumerating k-Matchings in Cyclic Chains Using the Transfer Matrix Technique
Simon Grad, Sandi Klavžar · match Communications in Mathematical and in Computer Chemistry · 2025
A cyclic chain is a plane graph whose all inner faces are cycles and its inner dual is isomorphic to a path. In this paper, the transfer matrix technique using the k-matching vector is developed to compute the number of k-matchings in an arbitrary cyclic chain. This extends similar methods developed earlier in two papers for benzenoid chains and for octagonal chains. The method is illustrated on the flourene molecule.