{"title":"High-order spectral characterizations of graphs","authors":"Lixiang Chen , Lizhu Sun , Changjiang Bu","doi":"10.1016/j.disc.2025.114421","DOIUrl":null,"url":null,"abstract":"<div><div>The tensor spectra of the power hypergraph of a graph <em>G</em> is called the high-order spectra of <em>G</em>. In this paper, we show that all Smith graphs are determined by their high-order spectra. We give some high-order cospectral invariants of trees and use them to show that some cospectral trees constructed by the classical Schwenk method can be distinguished by their high-order spectra.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 6","pages":"Article 114421"},"PeriodicalIF":0.7000,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X25000299","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
The tensor spectra of the power hypergraph of a graph G is called the high-order spectra of G. In this paper, we show that all Smith graphs are determined by their high-order spectra. We give some high-order cospectral invariants of trees and use them to show that some cospectral trees constructed by the classical Schwenk method can be distinguished by their high-order spectra.
期刊介绍：
Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory.
Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.
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