Geodesic
On diameter~$5$ trees with the maximum number of matchings
Sbornik. Mathematics, Tome 214 (2023) no. 2, pp. 273-284

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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: extremal graph theory, matching, tree. 
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     title = {On diameter~$5$ trees with the maximum number of matchings},
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N. A. Kuz'min; D. S. Malyshev. On diameter~$5$ trees with the maximum number of matchings. Sbornik. Mathematics, Tome 214 (2023) no. 2, pp. 273-284. http://geodesic.mathdoc.fr/item/SM_2023_214_2_a6/