{"title":"Bell图是由它们的拉普拉斯谱决定的","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":1.0000,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"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\":1.0000,\"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}","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}
Bell Graphs are Determined by their Laplacian Spectra
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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