{"title":"Constructing adjacency and distance cospectral graphs via regular rational orthogonal matrix","authors":"Lihuan Mao , Yuanhang Xu , Fenjin Liu , Bei Liu","doi":"10.1016/j.laa.2025.01.033","DOIUrl":null,"url":null,"abstract":"<div><div>Two graphs <em>G</em> and <em>H</em> are <em>cospectral</em> if they share the same spectrum. Constructing <em>cospectral</em> non-isomorphic graphs has been studied extensively for many years and various constructions are known in the literature. In this paper, we construct infinite families of adjacency cospectral graphs through the GM-switching method based on generalized Johnson graphs. We give some graph operations (e.g. rooted-product, corona, cartesian product, and coalescence) to construct distance cospectral graphs with different edges via a regular rational orthogonal matrix.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"710 ","pages":"Pages 111-128"},"PeriodicalIF":1.0000,"publicationDate":"2025-01-28","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/S0024379525000394","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
Two graphs G and H are cospectral if they share the same spectrum. Constructing cospectral non-isomorphic graphs has been studied extensively for many years and various constructions are known in the literature. In this paper, we construct infinite families of adjacency cospectral graphs through the GM-switching method based on generalized Johnson graphs. We give some graph operations (e.g. rooted-product, corona, cartesian product, and coalescence) to construct distance cospectral graphs with different edges via a regular rational orthogonal matrix.
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.
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