Átila Jones , Vilmar Trevisan , Cybele T.M. Vinagre
{"title":"Characterization of quasi-threshold graphs with two main Q-eigenvalues","authors":"Átila Jones , Vilmar Trevisan , Cybele T.M. Vinagre","doi":"10.1016/j.laa.2025.02.009","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we provide a structural description of certain connected cographs having <span><math><mi>k</mi><mo>≥</mo><mn>2</mn></math></span> main signless Laplacian eigenvalues. This result allows us to characterize the cographs which are <em>quasi</em>-threshold graphs with two main <strong>Q</strong>-eigenvalues. In addition, we describe all the <em>quasi</em>-threshold graphs belonging to the subclass of generalized core-satellite graphs with <span><math><mi>k</mi><mo>≥</mo><mn>2</mn></math></span> main <strong>Q</strong>-eigenvalues.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"711 ","pages":"Pages 68-83"},"PeriodicalIF":1.0000,"publicationDate":"2025-02-10","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/S002437952500059X","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
In this paper, we provide a structural description of certain connected cographs having main signless Laplacian eigenvalues. This result allows us to characterize the cographs which are quasi-threshold graphs with two main Q-eigenvalues. In addition, we describe all the quasi-threshold graphs belonging to the subclass of generalized core-satellite graphs with main Q-eigenvalues.
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.