{"title":"The full P-vertex problem for unicyclic graphs","authors":"A. Howlader, P.R. Raickwade, K.C. Sivakumar","doi":"10.1016/j.laa.2025.02.024","DOIUrl":null,"url":null,"abstract":"<div><div>Let <em>A</em> be a real symmetric and nonsingular matrix and <em>G</em> be the underlying graph. Let <span><math><mi>A</mi><mo>(</mo><mi>i</mi><mo>)</mo></math></span> be the principal submatrix obtained by removing the <span><math><msup><mrow><mi>i</mi></mrow><mrow><mtext>th</mtext></mrow></msup></math></span> row and the <span><math><msup><mrow><mi>i</mi></mrow><mrow><mtext>th</mtext></mrow></msup></math></span> column of <em>A</em>. If the nullity of <span><math><mi>A</mi><mo>(</mo><mi>i</mi><mo>)</mo></math></span> is unity, then the vertex <span><math><msub><mrow><mi>v</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> is called a P-vertex of the matrix <em>A</em>. The full P-vertex problem is to determine if there is a nonsingular matrix <em>A</em> such that each vertex of the corresponding graph <em>G</em>, is a P-vertex of <em>A</em>. In this article, we investigate the full P-vertex problem for unicyclic graphs.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"713 ","pages":"Pages 74-89"},"PeriodicalIF":1.0000,"publicationDate":"2025-03-06","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/S0024379525000874","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
Let A be a real symmetric and nonsingular matrix and G be the underlying graph. Let be the principal submatrix obtained by removing the row and the column of A. If the nullity of is unity, then the vertex is called a P-vertex of the matrix A. The full P-vertex problem is to determine if there is a nonsingular matrix A such that each vertex of the corresponding graph G, is a P-vertex of A. In this article, we investigate the full P-vertex problem for unicyclic graphs.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
