{"title":"Fractional perfect matching and distance spectral radius in graphs","authors":"Lei Zhang , Yaoping Hou , Haizhen Ren","doi":"10.1016/j.laa.2024.12.016","DOIUrl":null,"url":null,"abstract":"<div><div>A fractional matching of a graph <em>G</em> is a function <em>f</em> giving each edge a number in <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> so that <span><math><msub><mrow><mo>∑</mo></mrow><mrow><mi>e</mi><mo>∈</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>v</mi><mo>)</mo></mrow></msub><mi>f</mi><mo>(</mo><mi>e</mi><mo>)</mo><mo>≤</mo><mn>1</mn></math></span> for each <span><math><mi>v</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, where <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>v</mi><mo>)</mo></math></span> is the set of edges incident to <em>v</em>. In this paper, we give a distance spectral radius condition to guarantee the existence of a fractional perfect matching. This result generalize the result of Lin and Zhang (2021) <span><span>[22]</span></span>.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"708 ","pages":"Pages 480-488"},"PeriodicalIF":1.0000,"publicationDate":"2024-12-19","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/S0024379524004889","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
Abstract
A fractional matching of a graph G is a function f giving each edge a number in so that for each , where is the set of edges incident to v. In this paper, we give a distance spectral radius condition to guarantee the existence of a fractional perfect matching. This result generalize the result of Lin and Zhang (2021) [22].
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.