{"title":"Characterization of strongly regular integral circulant graphs by spectral approach","authors":"Milan Basic","doi":"10.2298/aadm180713023b","DOIUrl":null,"url":null,"abstract":"The integral circulant graph ICGn(D) has the vertex set Zn = {0, 1, 2, . . . , n? 1} and vertices a and b are adjacent if gcd(a ? b, n) ? D, where D ? Dn, Dn = {d : d | n, 1 ? d < n}. Motivated by the incorrect proof of a previously published result, in this paper we characterize the class of integral circulant graphs that are strongly regular. More precisely, connected ICGn(D) is strongly regular if and only if n is composite and D = {d ? Dn | m ? d} for some m | n and n ? 1 ? m ? 2.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applicable Analysis and Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2298/aadm180713023b","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3
Abstract
The integral circulant graph ICGn(D) has the vertex set Zn = {0, 1, 2, . . . , n? 1} and vertices a and b are adjacent if gcd(a ? b, n) ? D, where D ? Dn, Dn = {d : d | n, 1 ? d < n}. Motivated by the incorrect proof of a previously published result, in this paper we characterize the class of integral circulant graphs that are strongly regular. More precisely, connected ICGn(D) is strongly regular if and only if n is composite and D = {d ? Dn | m ? d} for some m | n and n ? 1 ? m ? 2.
期刊介绍：
Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).
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