On diameter $5$ trees with the maximum number of matchings

IF 0.8 4区数学 Q2 MATHEMATICS

Sbornik Mathematics Pub Date : 2023-01-01 DOI:10.4213/sm9745e

N. A. Kuz’min, D. Malyshev

引用次数: 0

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.

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在直径$5$的树上有最大数目的匹配

图中的匹配是图中没有公共顶点的任何边的集合。图的匹配数，又称细谷指数，是一个重要的参数，在数学化学中有着广泛的应用。在此之前，已经完全解决了固定大小的半径$2$(即直径$4$)树的Hosoya指数最大化问题。本文研究了直径$5$树在固定数目$n$顶点上的Hosoya指数最大化问题，并完全解决了这一问题。对于任意n，极值树都是唯一的。参考书目:6篇。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Sbornik Mathematics 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in: Mathematical analysis Ordinary differential equations Partial differential equations Mathematical physics Geometry Algebra Functional analysis