The Laplacian spectral radius of some bipartite graphs

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 K-1,K-k and one vertex of degree n of K-m,K-n, we denote by K-m,n(k) the resulting graph. We show that the graph K-2,n-k-2(k) (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 K-2,3(n-5) (n >= 7) is the unique graph with the largest Laplacian spectral radius among all the bicyclic bipartite graphs. (c) 2007 Elsevier Inc. All rights reserved.