Spectral radius of bipartite graphs
Copyright policy )Spectral radius of bipartite graphs
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 Kp,q of bipartition orders p and q by deleting k edges is attained when the deleting 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.
spectral radius, degree sequence, Extremal problems in graph theory, Eigenvalues, singular values, and eigenvectors, Distance in graphs, adjacency matrix, Graphs and linear algebra (matrices, eigenvalues, etc.), 05C50, 15A18, bipartite graph, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)
spectral radius, degree sequence, Extremal problems in graph theory, Eigenvalues, singular values, and eigenvectors, Distance in graphs, adjacency matrix, Graphs and linear algebra (matrices, eigenvalues, etc.), 05C50, 15A18, bipartite graph, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)
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