{"title":"Bell Graphs are Determined by their Laplacian Spectra","authors":"A. Z. Abdian","doi":"10.46793/kgjmat2302.203a","DOIUrl":null,"url":null,"abstract":"A graph G is said to be determined by the spectrum of its Laplacian spectrum (DLS, for short) if every graph with the same spectrum is isomorphic to G. An ∞-graph is a graph consisting of two cycles with just a vertex in common. Consider the coalescence of an ∞-graph and the star graph K1,s, with respect to their unique maximum degree. We call this a bell graph. In this paper, we aim to prove that all bell graphs are DLS.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kragujevac Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46793/kgjmat2302.203a","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
A graph G is said to be determined by the spectrum of its Laplacian spectrum (DLS, for short) if every graph with the same spectrum is isomorphic to G. An ∞-graph is a graph consisting of two cycles with just a vertex in common. Consider the coalescence of an ∞-graph and the star graph K1,s, with respect to their unique maximum degree. We call this a bell graph. In this paper, we aim to prove that all bell graphs are DLS.
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