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The Laplacian spectral radius of some bipartite graphs
Authors:Xiaoling Zhang
Institution:School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, PR China
Abstract: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 View the MathML source the resulting graph. We show that the graph View the MathML source(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 View the MathML source(n?7) is the unique graph with the largest Laplacian spectral radius among all the bicyclic bipartite graphs.
Keywords:05C50  15A18
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