Laplacian spectra and invariants of graphs (Q1850006)

Let \(b(G)=(n-1)/(1/\lambda_2 + 1/\lambda_3 + \dots + 1/\lambda_n)\) be the harmonic mean of positive Laplacian eigenvalues \(\lambda_2, \lambda_3, \dots, \lambda_n\) of a connected graph \(G\) with \(n\) vertices. The author gives bounds for the minimal edge-density in edge-cuts, edge-connectivity, isoperimetric number, average distance, average length of the longest path between pairs of vertices and edge-forwarding index in terms of \(b(G)\), thus improving some of known results in the literature.