{"title":"Laplacian energy of trees with at most 10 vertices","authors":"M. U. Rehman, M. Ajmal, T. Kamran","doi":"10.19184/IJC.2018.2.1.3","DOIUrl":null,"url":null,"abstract":"Let T<sub>n</sub> be the set of all trees with n ≤ 10 vertices. We show that the Laplacian energy of any tree T<sub>n</sub> is strictly between the Laplacian energy of the path Pn and the star S<sub>n</sub>, partially proving the conjecture that this hold for any tree.","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"52 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2018-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indonesian Journal of Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.19184/IJC.2018.2.1.3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Let Tn be the set of all trees with n ≤ 10 vertices. We show that the Laplacian energy of any tree Tn is strictly between the Laplacian energy of the path Pn and the star Sn, partially proving the conjecture that this hold for any tree.
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