An Upper Bound on the Spectral Radius of Weighted Graphs
نویسندگان
چکیده
We consider weighted graphs, where the edge weights are positive definite matrices. The eigenvalues of a graph are the eigenvalues of its adjacency matrix. We obtain another upper bound which is sharp on the spectral radius of the adjacency matrix and compare with some known upper bounds with the help of some examples of graphs. We also characterize graphs for which the bound is attained.
منابع مشابه
A sharp upper bound on the spectral radius of weighted graphs
We consider weighted graphs, where the edgeweights are positive definite matrices. The eigenvalues of a graph are the eigenvalues of its adjacency matrix. We obtain an upper bound on the spectral radius of the adjacency matrix and characterize graphs for which the bound is attained. © 2007 Elsevier B.V. All rights reserved.
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