Properties and applications of the eigenvector corresponding to the Laplacian spectral radius of a graph (Q460047)

Summary: We study the properties of the eigenvector corresponding to the Laplacian spectral radius of a graph and show some applications. We obtain some results on the Laplacian spectral radius of a graph by grafting and adding edges. We also determine the structure of the maximal Laplacian spectrum tree among trees with \(n\) vertices and \(k\) pendant vertices (\(n\), \(k\) fixed), and the upper bound of the Laplacian spectral radius of some trees.