The Laplacian spectral radius of some bipartite graphs

AbstractIn this paper, we study the largest Laplacian spectral radius of the bipartite graphs with n vertices and k cut edges and the bicyclic bipartite graphs, respectively. Identifying the center of a star K1,k and one vertex of degree n of Km,n, we denote by Km,nk the resulting graph. We show that the graph K2,n-k-2k (1⩽k⩽n-4) is the unique graph with the largest Laplacian spectral radius among the bipartite graphs with n vertices and k cut edges, and K2,3n-5 (n⩾7) is the unique graph with the largest Laplacian spectral radius among all the bicyclic bipartite graphs