On the Laplacian spectral ratio of connected graphs

The Laplacian spectrum of a graph is the eigenvalues of the associated Laplacian matrix. The quotient between the largest and second smallest Laplacian eigenvalues of a connected graph, is called the Laplacian spectral ratio. Some bounds on the Laplacian spectral ratio are considered. We improve a relation on the Laplacian spectral ratio of regular graphs. Especially, the first two smallest Laplacian spectral ratios of graphs with given order are determined. And some operations on Laplacian spectral ratio are presented.