Comparison between Kirchhoff index and the Laplacian-energy-like invariant

Let G be a connected graph of order n with Laplacian eigenvalues μ1⩾μ2⩾⋯⩾μn-1>μn=0. The Kirchhoff index and the Laplacian-energy-like invariant of G are defined as and , respectively. We compare Kf and LEL and establish two sufficient conditions under which LELKf holds.