{"title":"On 5- and 6-Leaved Trees with the Largest Number of Matchings","authors":"N. A. Kuz’min, D. S. Malyshev","doi":"10.1134/s0001434624030064","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> A matching of a graph is a set of its edges that pairwise do not have common vertices. An important parameter of graphs, which is used in mathematical chemistry, is the Hosoya index, defined as the number of their matchings. Previously, the problems of maximizing this index were considered and completely solved for <span>\\(n\\)</span>-vertex trees with two, three and four leaves for any sufficiently large <span>\\(n\\)</span>. In the present paper, a similar problem is completely solved for 5-leaved trees with <span>\\(n\\geq 20\\)</span> and for 6-leaved trees with <span>\\(n\\geq 26\\)</span>. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Notes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0001434624030064","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
A matching of a graph is a set of its edges that pairwise do not have common vertices. An important parameter of graphs, which is used in mathematical chemistry, is the Hosoya index, defined as the number of their matchings. Previously, the problems of maximizing this index were considered and completely solved for \(n\)-vertex trees with two, three and four leaves for any sufficiently large \(n\). In the present paper, a similar problem is completely solved for 5-leaved trees with \(n\geq 20\) and for 6-leaved trees with \(n\geq 26\).
期刊介绍：
Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.
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