Computing the Number of s-Matchings in Cyclooctatetraene Chains

Abstract

The Hosoya index is an important topological index in graph theory, which is defined as the total number of s-matchings, denoted as m(G,s), in a graph G. Therefore, computing the number of s-matchings for various molecular structures holds significant importance. By applying the concept of symmetry, defining the s-matching vector of the graph with a specified edge, using the transfer matrix, and iteratively applying two recursive formulas to derive the reduction formula, we compute the number of s-matchings of cyclooctatetraene chains.