{"title":"正则图的负特征值","authors":"Wen-Ching Winnie Li","doi":"10.1016/S0764-4442(01)02155-3","DOIUrl":null,"url":null,"abstract":"<div><p>In this Note we prove that if {<em>G</em><sub><em>n</em></sub>} is a sequence of connected <em>k</em>-regular graphs in which the length of odd cycles approaches infinity as <em>n</em>→∞, then the <span><math><mtext>lim</mtext><mspace></mspace><mtext>sup</mtext></math></span> of the smallest eigenvalue of <em>G</em><sub><em>n</em></sub> greater than −<em>k</em> is at most <span><math><mtext>−2</mtext><mtext>k−1</mtext></math></span> as <em>n</em> tends to infinity.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 10","pages":"Pages 907-912"},"PeriodicalIF":0.0000,"publicationDate":"2001-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02155-3","citationCount":"11","resultStr":"{\"title\":\"On negative eigenvalues of regular graphs\",\"authors\":\"Wen-Ching Winnie Li\",\"doi\":\"10.1016/S0764-4442(01)02155-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this Note we prove that if {<em>G</em><sub><em>n</em></sub>} is a sequence of connected <em>k</em>-regular graphs in which the length of odd cycles approaches infinity as <em>n</em>→∞, then the <span><math><mtext>lim</mtext><mspace></mspace><mtext>sup</mtext></math></span> of the smallest eigenvalue of <em>G</em><sub><em>n</em></sub> greater than −<em>k</em> is at most <span><math><mtext>−2</mtext><mtext>k−1</mtext></math></span> as <em>n</em> tends to infinity.</p></div>\",\"PeriodicalId\":100300,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"volume\":\"333 10\",\"pages\":\"Pages 907-912\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02155-3\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0764444201021553\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0764444201021553","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this Note we prove that if {Gn} is a sequence of connected k-regular graphs in which the length of odd cycles approaches infinity as n→∞, then the of the smallest eigenvalue of Gn greater than −k is at most as n tends to infinity.
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