Computing the number of k-matchings in benzenoid chains

Abstract

The Hosoya index is associated with many thermodynamic properties such as boiling point, entropy, total pi-electron energy. Transfer matrix technique is extensively utilized in mathematical chemistry for various enumeration problems. In this paper, we introduce the k-matching vector at a certain edge of graph G. Then by using the k-matching vector and two recurrence formulas, we get reduction formulas to compute k-matching number p(G, k) of any benzenoid chains for for all k >= 0 whose summation gives the Hosoya index of the chain. In conclusion, we compute p(G, k) of any benzenoid chains via an appropriate multiplication of three 4(k+ 1) x4(k+ 1) dimensional transfer matrices and a terminal vector which can be obtained by given two algorithms.