Extremal graph characterization from the bounds of the spectral radius of weighted graphs |
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| Authors: | Kinkar Ch. Das |
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| Affiliation: | Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea |
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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 a lower bound and an upper bound on the spectral radius of the adjacency matrix of weighted graphs and characterize graphs for which the bounds are attained. |
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| Keywords: | Weighted graph Adjacency matrix Spectral radius Upper bound Lower bound |
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