Abstract
The Hosoya index of \(G\) is defined as the total number of independent edge sets (number of \(k\)-matchings \(p(G,k)\)) in \(G\). The Hosoya index is one of the most important topological indices in the field of mathematical chemistry because of its
relationship with several thermodynamic properties. Therefore, computation of the number of \(k\)-matchings of various molecular structures has importance. Two methods, one for computing the number of the Hosoya index of catacondensed
benzenoid systems and the other for the number of \(k\)-matchings in benzenoid chains (unbranched catacondensed benzenoid systems), have been presented so far. In this paper, a method based on some transfer matrices to compute the number
of \(k\)-matchings of arbitrary (both unbranched and branched) catacondensed benzenoid systems is presented. Moreover, some algorithms are designed to keep the applicability of the method the same as \(k\) increases.
