A sharp upper bound on the spectral radius of weighted graphs |
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| Authors: | Kinkar Ch. Das R.B. Bapat |
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| Affiliation: | a Combinatorial and Computational Mathematics Center, Mathematics, Pohang University of Science and Technology, Pohang 790-784, South Korea
b Indian Statistical Institute, New Delhi 110016, India |
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| Abstract: | 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 an upper bound on the spectral radius of the adjacency matrix and characterize graphs for which the bound is attained. |
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| Keywords: | Weighted graph Adjacency matrix Spectral radius Upper bound |
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