Comparison between the laplacian–energy–like invariant and the kirchhoff index

Abstract

© 2016, International Linear Algebra Society. All Rights Reserved. For a simple connected graph G of order n, having Laplacian eigenvalues μ1, μ2, …, μn−1, μn = 0, the Laplacian–energy–like invariant (LEL) and the Kirchhoff index (Kf) are defined as LEL(G) = Σn−1i=1 √μi and Kf(G) = nΣn−1i=1 1/μi, respectively. In this paper, LEL and Kf are compared, and sufficient conditions for the inequality Kf(G) < LEL(G) are established.