Email this article On diameter $5$ trees with the maximum number of matchings
- Authors: Kuz'min N.A.1, Malyshev D.S.1
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Affiliations:
- National Research University – Higher School of Economics in Nizhny Novgorod
- Issue: Vol 214, No 2 (2023)
- Pages: 143-154
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/133519
- DOI: https://doi.org/10.4213/sm9745
- ID: 133519
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Abstract
A matching in a graph is any set of edges of this graph without common vertices. The number of matchings, also known as the Hosoya index of the graph, is an important parameter, which finds wide applications in mathematical chemistry. Previously, the problem of maximizing the Hosoya index in trees of radius $2$ (that is, diameter $4$) of fixed size was completely solved. This work considers the problem of maximizing the Hosoya index in trees of diameter $5$ on a fixed number $n$ of vertices and solves it completely. It turns out that for any $n$ the extremal tree is unique. Bibliography: 6 titles.
Keywords
About the authors
Nikita Aleksandrovich Kuz'min
National Research University – Higher School of Economics in Nizhny Novgorod
Email: nikita.kuz2000@gmail.com
Dmitriy Sergeevich Malyshev
National Research University – Higher School of Economics in Nizhny Novgorod
Email: dsmalyshev@rambler.ru
Doctor of physico-mathematical sciences, Professor
References
- H. Hosoya, “Topological index. A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons”, Bull. Chem. Soc. Japan, 44:9 (1971), 2332–2339
- H. Hosoya, “The topological index $Z$ before and after 1971”, Internet Electron. J. Mol. Des., 1:9 (2002), 428–442
- H. Hosoya, “Important mathematical structures of the topological index $Z$ for tree graphs”, J. Chem. Inf. Model., 47:3 (2007), 744–750
- H. Hosoya, “Mathematical meaning and importance of the topological index $Z$”, Croat. Chem. Acta, 80:2 (2007), 239–249
- Н. А. Кузьмин, “О деревьях радиуса 2 с максимальным количеством паросочетаний”, Журнал СВМО, 22:2 (2020), 177–187
- Н. А. Кузьмин, Д. C. Малышев, “Новое доказательство результата о полном описании $(n,n+2)$-графов c максимальным значением индекса Хосойи”, Матем. заметки, 111:2 (2022), 258–276
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