Some remarks on Laplacian eigenvalues of connected graphs

Let G be a connected undirected graph with n vertices and m   edges, and let μ1≥μ2≥…≥μn−1>μn=0μ1≥μ2≥…≥μn−1>μn=0 be Laplacian eigenvalues of adjacency matrix of G  . In this paper a generalization of some inequalities for the Laplacian spreads LS(G)=μ1−μn−1LS(G)=μ1−μn−1, LR+(G)=μ1μn−1+μn−1μ1 and LR−(G)=μ1μn−1−μn−1μ1 is presented.