{"title":"关于树的拉普拉斯特征值的多重性的注记","authors":"Zhenye Xu, Chun Yang","doi":"10.1109/ICACIA.2009.5361147","DOIUrl":null,"url":null,"abstract":"Considering the multiplicity m<inf>T</inf> (λ) of eigenvalue λ (which equals 1) of Laplacian matrix of all trees, we get three results: When m<inf>T</inf> (1) equals n-2, the tree is unique, that is star graph K<inf>1,n-1</inf>; (ii) there exists no trees satisfying m<inf>T</inf> (1) equals n-3; (iii) When m<inf>T</inf> (1) equals n-4, this kind of trees are divided into two types. According to the process of proving, we devise a method to construct trees on some desired properties, which have practical value.","PeriodicalId":423210,"journal":{"name":"2009 International Conference on Apperceiving Computing and Intelligence Analysis","volume":"21 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A note on multiplicity of the Laplacian eigenvalue of trees\",\"authors\":\"Zhenye Xu, Chun Yang\",\"doi\":\"10.1109/ICACIA.2009.5361147\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Considering the multiplicity m<inf>T</inf> (λ) of eigenvalue λ (which equals 1) of Laplacian matrix of all trees, we get three results: When m<inf>T</inf> (1) equals n-2, the tree is unique, that is star graph K<inf>1,n-1</inf>; (ii) there exists no trees satisfying m<inf>T</inf> (1) equals n-3; (iii) When m<inf>T</inf> (1) equals n-4, this kind of trees are divided into two types. According to the process of proving, we devise a method to construct trees on some desired properties, which have practical value.\",\"PeriodicalId\":423210,\"journal\":{\"name\":\"2009 International Conference on Apperceiving Computing and Intelligence Analysis\",\"volume\":\"21 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-12-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2009 International Conference on Apperceiving Computing and Intelligence Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICACIA.2009.5361147\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 International Conference on Apperceiving Computing and Intelligence Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICACIA.2009.5361147","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A note on multiplicity of the Laplacian eigenvalue of trees
Considering the multiplicity mT (λ) of eigenvalue λ (which equals 1) of Laplacian matrix of all trees, we get three results: When mT (1) equals n-2, the tree is unique, that is star graph K1,n-1; (ii) there exists no trees satisfying mT (1) equals n-3; (iii) When mT (1) equals n-4, this kind of trees are divided into two types. According to the process of proving, we devise a method to construct trees on some desired properties, which have practical value.
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