On Laplacian energy in terms of graph invariants.

For G being a graph with n vertices and m edges, and with Laplacian eigenvalues μ 1 ≥ μ 2 ≥ ⋯ ≥ μ n − 1 ≥ μ n = 0 , the Laplacian energy is defined as L E = ∑ i = 1 n | μ i − 2 m / n | . Let σ be the largest positive integer such that μ σ ≥ 2 m / n . We characterize the graphs satisfying σ = n − 1 . Using this, we obtain lower bounds for LE in terms of n, m , and the first Zagreb index. In addition, we present some upper bounds for LE in terms of graph invariants such as n, m , maximum degree, vertex cover number, and spanning tree packing number. [ABSTRACT FROM AUTHOR]