细分和图特征值

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-02-04 DOI:10.1016/j.laa.2025.01.044

Hitesh Kumar, Bojan Mohar , Shivaramakrishna Pragada, Hanmeng Zhan

{"title":"细分和图特征值","authors":"Hitesh Kumar, Bojan Mohar , Shivaramakrishna Pragada, Hanmeng Zhan","doi":"10.1016/j.laa.2025.01.044","DOIUrl":null,"url":null,"abstract":"<div><div>This paper investigates the asymptotic nature of graph spectra when some edges of a graph are subdivided sufficiently many times. In the special case where all edges of a graph are subdivided, we find the exact limits of the <em>k</em>-th largest and <em>k</em>-th smallest eigenvalues for any fixed <em>k</em>. Given a graph, we show that after subdividing sufficiently many times, all but <span><math><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span> eigenvalues of the new graph will lie in the interval <span><math><mo>[</mo><mo>−</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>]</mo></math></span>. We examine the eigenvalues of the new graph outside this interval, and we prove several results that might be of independent interest.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"710 ","pages":"Pages 336-355"},"PeriodicalIF":1.0000,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Subdivision and graph eigenvalues\",\"authors\":\"Hitesh Kumar, Bojan Mohar , Shivaramakrishna Pragada, Hanmeng Zhan\",\"doi\":\"10.1016/j.laa.2025.01.044\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This paper investigates the asymptotic nature of graph spectra when some edges of a graph are subdivided sufficiently many times. In the special case where all edges of a graph are subdivided, we find the exact limits of the <em>k</em>-th largest and <em>k</em>-th smallest eigenvalues for any fixed <em>k</em>. Given a graph, we show that after subdividing sufficiently many times, all but <span><math><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span> eigenvalues of the new graph will lie in the interval <span><math><mo>[</mo><mo>−</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>]</mo></math></span>. We examine the eigenvalues of the new graph outside this interval, and we prove several results that might be of independent interest.</div></div>\",\"PeriodicalId\":18043,\"journal\":{\"name\":\"Linear Algebra and its Applications\",\"volume\":\"710 \",\"pages\":\"Pages 336-355\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2025-02-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Linear Algebra and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0024379525000503\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Linear Algebra and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0024379525000503","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文研究了当图的某些边被足够多次细分时图谱的渐近性质。在图的所有边都被细分的特殊情况下，我们找到了任意固定k的第k大和第k小特征值的精确极限。给定一个图，我们证明了在细分足够多次后，新图的所有特征值除了O(1)之外都位于区间[−2,2]。我们检验了新图在这个区间外的特征值，并证明了几个可能独立感兴趣的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Subdivision and graph eigenvalues

This paper investigates the asymptotic nature of graph spectra when some edges of a graph are subdivided sufficiently many times. In the special case where all edges of a graph are subdivided, we find the exact limits of the k-th largest and k-th smallest eigenvalues for any fixed k. Given a graph, we show that after subdividing sufficiently many times, all but

O (1)

eigenvalues of the new graph will lie in the interval

[- 2, 2]

. We examine the eigenvalues of the new graph outside this interval, and we prove several results that might be of independent interest.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.