Extremal trees with fixed order and diameter for average size of maximal matchings

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-08-20 DOI:10.1016/j.dam.2025.08.016

Lukai Sui, Qiuli Li

引用次数: 0

Abstract

This paper characterizes the classes of graphs whose average sizes of maximal matchings achieve the extremum in trees with fixed order and diameter. Regarding the conjecture posed by Engbers and Erey about the minimum case, we confirm it for trees of fixed order with diameters 6, 7 and 8. Furthermore, we also confirm the conjecture for the maximum case in trees of fixed order with diameter 6. Our proofs base on a meticulous analysis of graph structures and a thorough exploration of matching theory. By studying trees with different diameters, we discover some interesting properties and patterns, which provide insights for further research.

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对于最大匹配的平均大小，具有固定顺序和直径的极值树

本文刻画了在定阶定径树中最大匹配的平均大小达到极值的图的类别。关于Engbers和Erey关于最小情况的猜想，我们对直径为6、7和8的定阶树进行了验证。此外，我们还证实了直径为6的定阶树的极大值情况的猜想。我们的证明基于对图结构的细致分析和对匹配理论的深入探索。通过研究不同直径的树，我们发现了一些有趣的特性和模式，为进一步的研究提供了见解。

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

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.