饱和无覆盖图的大小和谱半径

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-07-23 DOI:10.1016/j.dam.2025.07.029

Zeyuan Wu , Hongzhang Chen , Jianxi Li

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引用次数: 0

摘要

图G=（V，E）是一个匹配覆盖图，如果对于每一个E∈E(G)，存在至少一个G的完美匹配M使得E∈M。偶阶图G是饱和非覆盖图，如果对于任意e∈e （G¯），G+e是匹配覆盖图，而G不是。最近，Zhou， Cao和Yan（2025）提供了饱和非覆盖图的结构表征。本文从饱和非覆盖图的大小和特征值两个方面进一步研究了饱和非覆盖图。在所有饱和非覆盖图中分别识别出了最大尺寸图和最大谱半径图，并建立了饱和非覆盖图的拉普拉斯特征比的上界。

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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The size and the spectral radius of a saturated non-covered graph

A graph

G = (V, E)

is a matching-covered graph if for every

e \in E (G)

, there exists at least one perfect matching

M

G

such that

e \in M

. A graph

G

of even order is a saturated non-covered graph if for any

e \in E (\bar{G})

G + e

is a matching-covered graph but

G

is not. Very recently, Zhou, Cao and Yan (2025) provided a structural characterization on the saturated non-covered graphs. In this paper, we further study the saturated non-covered graph from its size and eigenvalues. The graphs with the maximum size and the maximum spectral radius among all saturated non-covered graphs are identified, respectively, as well as an upper bound on the Laplacian eigenratio of a saturated non-covered graph is also established.

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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.