On the lower bound for Laplacian resolvent energy through majorization

Abstract

For a simple connected graph [Formula: see text] of order [Formula: see text] with Laplacian eigenvalues [Formula: see text], the Laplacian resolvent energy of [Formula: see text] is defined as [Formula: see text] In this paper, we provide an improved lower bound for [Formula: see text] through majorization. Considering our lower bound, we also derive some lower bounds for [Formula: see text] when the graph [Formula: see text] possesses tree structure.