On the lower bound for Laplacian resolvent energy through majorization

For a simple connected graph G of order n with Laplacian eigenvalues μ1 ≥ μ2 ≥ · · · ≥ μn−1 > μn = 0, the Laplacian resolvent energy of G is defined as RL(G) = \sumni=1 n+11−μi . In this paper, we provide an improved lower bound for RL(G) through majorization. Considering our lower bound, we also derive some lower bounds for RL(G) when the graph G possesses tree structure.