关于匹配数最多的五叶树和六叶树

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-05 DOI:10.1134/s0001434624030064

N. A. Kuz’min, D. S. Malyshev

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引用次数: 0

摘要

摘要图的匹配是指图中没有共同顶点的成对边的集合。在数学化学中，图的一个重要参数是细谷指数（Hosoya index），它被定义为图的匹配数。在此之前，对于任意足够大的\(n\)，具有两叶、三叶和四叶的\(n\)-顶点树，已经考虑并完全解决了最大化该指数的问题。在本文中，一个类似的问题被完全解决了，即对于有5片叶子的树（\(n\geq 20\) 和有\(n\geq 26\) 的6片叶子的树（\(n\geq 26\) ）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On 5- and 6-Leaved Trees with the Largest Number of Matchings

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On 5- and 6-Leaved Trees with the Largest Number of Matchings

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 \(n\geq 26\).

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

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.