Computing the Number of k-Matchings in Benzenoid Chains
MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, vol.88, no.1, pp.79-92, 2022 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 88 Issue: 1
- Publication Date: 2022
- Doi Number: 10.46793/match.88-1.079o
- Journal Name: MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
- Page Numbers: pp.79-92
- Open Archive Collection: AVESIS Open Access Collection
- Bursa Uludag University Affiliated: Yes
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.