Geodesic
On diameter $5$ trees with the maximum number of matchings
Sbornik. Mathematics, Tome 214 (2023) no. 2, pp. 273-284 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{SM_2023_214_2_a6,
     author = {N. A. Kuz'min and D. S. Malyshev},
     title = {On diameter~$5$ trees with the maximum number of matchings},
     journal = {Sbornik. Mathematics},
     pages = {273--284},
     year = {2023},
     volume = {214},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2023_214_2_a6/}
}
TY  - JOUR
AU  - N. A. Kuz'min
AU  - D. S. Malyshev
TI  - On diameter $5$ trees with the maximum number of matchings
JO  - Sbornik. Mathematics
PY  - 2023
SP  - 273
EP  - 284
VL  - 214
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_2023_214_2_a6/
LA  - en
ID  - SM_2023_214_2_a6
ER  - 
%0 Journal Article
%A N. A. Kuz'min
%A D. S. Malyshev
%T On diameter $5$ trees with the maximum number of matchings
%J Sbornik. Mathematics
%D 2023
%P 273-284
%V 214
%N 2
%U http://geodesic.mathdoc.fr/item/SM_2023_214_2_a6/
%G en
%F SM_2023_214_2_a6
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/

[1] 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 | DOI

[2] H. Hosoya, “The topological index $Z$ before and after 1971”, Internet Electron. J. Mol. Des., 1:9 (2002), 428–442

[3] H. Hosoya, “Important mathematical structures of the topological index $Z$ for tree graphs”, J. Chem. Inf. Model., 47:3 (2007), 744–750 | DOI

[4] H. Hosoya, “Mathematical meaning and importance of the topological index $Z$”, Croat. Chem. Acta, 80:2 (2007), 239–249

[5] N. A. Kuz'min, “Trees of radius 2 with the maximum number of matchings”, Zh. Srednevolzhsk. Mat. Obshch., 22:2 (2020), 177–187 (Russian) | DOI

[6] N. A. Kuz'min and D. S. Malyshev, “A new proof of a result concerning a complete description of $(n, n + 2)$-graphs with maximum value of the Hosoya index”, Mat. Zametki, 111:2 (2022), 258–276 ; English transl. in Math. Notes, 111:2 (2022), 258–272 | DOI | MR | Zbl | DOI