Maximizing the Laplacian spectral radii of graphs with given diameter

Let B(n,d) be the set of bipartite graphs with order n and diameter d. The extremal graph Gd with the maximal Laplacian spectral radius μ in B(n,d) is determined for each 1⩽d⩽n-1. As an application, we also determine all the general graphs with given diameter which have the maximal Laplacian spectral radii.