{"title":"A Method for Computing the Merrifield–Simmons Index on Benzenoid Systems","authors":"G. De Ita, Pedro Bello, Meliza Contreras","doi":"10.46793/match.89-1.245i","DOIUrl":null,"url":null,"abstract":"We present a method for computing the Merrifield-Simmons index on some basic graphs. For example, our proposal works on paths, simple cycles, trees, and we show that the method can be extended to process benzenoid systems Hr,t with a total of r.t hexagons. In the case of benzenoid systems, our method consists of performing a linear-time Hamiltonian walking on an isomorphic hexagonal grid from , at the same time that the number of independent sets are being computed incrementally. Our method improves the asymptotic behavior of the time-complexity with respect to the transfer matrix method, which is the classic method for computing the Merrifield-Simmons index on grid graphs, even for benzenoid systems.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Match-Communications in Mathematical and in Computer Chemistry","FirstCategoryId":"92","ListUrlMain":"https://doi.org/10.46793/match.89-1.245i","RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
We present a method for computing the Merrifield-Simmons index on some basic graphs. For example, our proposal works on paths, simple cycles, trees, and we show that the method can be extended to process benzenoid systems Hr,t with a total of r.t hexagons. In the case of benzenoid systems, our method consists of performing a linear-time Hamiltonian walking on an isomorphic hexagonal grid from , at the same time that the number of independent sets are being computed incrementally. Our method improves the asymptotic behavior of the time-complexity with respect to the transfer matrix method, which is the classic method for computing the Merrifield-Simmons index on grid graphs, even for benzenoid systems.
期刊介绍:
MATCH Communications in Mathematical and in Computer Chemistry publishes papers of original research as well as reviews on chemically important mathematical results and non-routine applications of mathematical techniques to chemical problems. A paper acceptable for publication must contain non-trivial mathematics or communicate non-routine computer-based procedures AND have a clear connection to chemistry. Papers are published without any processing or publication charge.