Spectral radius of bipartite graphs

Abstract

Let k, p, q be positive integers with k < p < q + 1. We prove that the maximum spectral radius of a simple bipartite graph obtained from the complete bipartite graph K-p,K-q of bipartition orders p and q by deleting k edges is attained when the deleted edges are all incident on a common vertex which is located in the partite set of order q. Our method is based on new sharp upper bounds on the spectral radius of bipartite graphs in terms of their degree sequences. (C) 2015 Elsevier Inc. All rights reserved.