{"title":"谱图理论","authors":"Amol Sahebrao Hinge","doi":"10.1090/cbms/129/05","DOIUrl":null,"url":null,"abstract":"Spectral graph theory is a vast and expanding area of combinatorics. We start these notes by introducing and motivating classical matrices associated with a graph, and then show how to derive combinatorial properties of a graph from the eigenvalues of these matrices. We then examine more modern results such as polynomial interlacing and high dimensional expanders","PeriodicalId":440287,"journal":{"name":"Zeta and 𝐿-functions in Number Theory and\n Combinatorics","volume":"42 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2194","resultStr":"{\"title\":\"Spectral graph theory\",\"authors\":\"Amol Sahebrao Hinge\",\"doi\":\"10.1090/cbms/129/05\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Spectral graph theory is a vast and expanding area of combinatorics. We start these notes by introducing and motivating classical matrices associated with a graph, and then show how to derive combinatorial properties of a graph from the eigenvalues of these matrices. We then examine more modern results such as polynomial interlacing and high dimensional expanders\",\"PeriodicalId\":440287,\"journal\":{\"name\":\"Zeta and 𝐿-functions in Number Theory and\\n Combinatorics\",\"volume\":\"42 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2194\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Zeta and 𝐿-functions in Number Theory and\\n Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/cbms/129/05\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zeta and 𝐿-functions in Number Theory and\n Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/cbms/129/05","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Spectral graph theory is a vast and expanding area of combinatorics. We start these notes by introducing and motivating classical matrices associated with a graph, and then show how to derive combinatorial properties of a graph from the eigenvalues of these matrices. We then examine more modern results such as polynomial interlacing and high dimensional expanders
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