{"title":"Remarks on \"Comparison between the Laplacian energy-like invariant and the Kirchhoff index''","authors":"Xiaodan Chen, Guoliang Hao","doi":"10.13001/ela.2022.6383","DOIUrl":null,"url":null,"abstract":"The Laplacian-energy-like invariant and the Kirchhoff index of an $n$-vertex simple connected graph $G$ are, respectively, defined to be $LEL(G)=\\sum_{i=1}^{n-1}\\sqrt{\\mu_i}$ and $Kf(G)=n\\sum_{i=1}^{n-1}\\frac{1}{\\mu_i}$, where $\\mu_1,\\mu_2,\\ldots,\\mu_{n-1},\\mu_n=0$ are the Laplacian eigenvalues of $G$. In this paper, some results in the paper [Comparison between the Laplacian-energy-like invariant and the Kirchhoff index. Electron. J. Linear Algebra 31:27-41, 2016] are corrected and improved.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2022-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Linear Algebra","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.13001/ela.2022.6383","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
The Laplacian-energy-like invariant and the Kirchhoff index of an $n$-vertex simple connected graph $G$ are, respectively, defined to be $LEL(G)=\sum_{i=1}^{n-1}\sqrt{\mu_i}$ and $Kf(G)=n\sum_{i=1}^{n-1}\frac{1}{\mu_i}$, where $\mu_1,\mu_2,\ldots,\mu_{n-1},\mu_n=0$ are the Laplacian eigenvalues of $G$. In this paper, some results in the paper [Comparison between the Laplacian-energy-like invariant and the Kirchhoff index. Electron. J. Linear Algebra 31:27-41, 2016] are corrected and improved.
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