The Laplacian spectral radius of some bipartite graphs Original Research Article

In 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 image the resulting graph. We show that the graph image (1less-than-or-equals, slantkless-than-or-equals, slantn-4) is the unique graph with the largest Laplacian spectral radius among the bipartite graphs with n vertices and k cut edges, and image (ngreater-or-equal, slanted7) is the unique graph with the largest Laplacian spectral radius among all the bicyclic bipartite graphs.