{"title":"Turán problem of signed graph for negative odd cycle","authors":"Junjie Wang , Yaoping Hou , Xueyi Huang","doi":"10.1016/j.dam.2024.11.024","DOIUrl":null,"url":null,"abstract":"<div><div>We investigate natural Turán problems on signed graphs in this paper. Let <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mn>2</mn><mi>k</mi><mo>+</mo><mn>1</mn></mrow><mrow><mo>−</mo></mrow></msubsup></math></span> denote the signed cycle of length <span><math><mrow><mn>2</mn><mi>k</mi><mo>+</mo><mn>1</mn></mrow></math></span> with one negative edge. We determine the maximum number of edges among all unbalanced signed graphs of order <span><math><mi>n</mi></math></span> with no subgraph switching to <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mn>2</mn><mi>k</mi><mo>+</mo><mn>1</mn></mrow><mrow><mo>−</mo></mrow></msubsup></math></span>, where <span><math><mrow><mn>3</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>10</mn></mrow></mfrac><mo>−</mo><mn>1</mn></mrow></math></span>, and characterize the extremal signed graphs. As a by-product, we also obtain the maximum spectral radius among these signed graphs.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"362 ","pages":"Pages 157-166"},"PeriodicalIF":1.0000,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166218X24004931","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We investigate natural Turán problems on signed graphs in this paper. Let denote the signed cycle of length with one negative edge. We determine the maximum number of edges among all unbalanced signed graphs of order with no subgraph switching to , where , and characterize the extremal signed graphs. As a by-product, we also obtain the maximum spectral radius among these signed graphs.
期刊介绍：
The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal.
Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.
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