Remarks on "Comparison between the Laplacian energy-like invariant and the Kirchhoff index''

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.