Lower bounds for the first eigenvalue of certain M-matrices associated with graphs (Q1194509)
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scientific article; zbMATH DE number 64481
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lower bounds for the first eigenvalue of certain M-matrices associated with graphs |
scientific article; zbMATH DE number 64481 |
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Lower bounds for the first eigenvalue of certain M-matrices associated with graphs (English)
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27 September 1992
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The author gives Cheeger type lower bounds [cf. \textit{J. Cheeger} [Probl. Anal. Symp. in Honor of Salomon Bochner, Princeton Univ. 1969, 195-199 (1970; Zbl 0212.449)] for the smallest eigenvalue of the Laplacian of corresponding undirected connected multigraphs in terms of the expansion coefficients and norm estimates. Upper bounds for the convergence rate of certain nonnegative irreducible symmetric matrices and irreducible diagonally symmetrizable stochastic matrices are also obtained.
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\(M\)-matrices
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lower bounds
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smallest eigenvalue
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Laplacian
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undirected connected multigraphs
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convergence rate
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nonnegative irreducible symmetric matrices
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irreducible diagonally symmetrizable stochastic matrices
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