Lower bounds for the first eigenvalue of certain M-matrices associated with graphs
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Abstract We give lower bounds 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 given.
[1] Mark Jerrum,et al. Approximate Counting, Uniform Generation and Rapidly Mixing Markov Chains , 1987, WG.
[2] Estimates of the spectral radius of graphs , 1993 .
[3] Gene H. Golub,et al. Matrix computations , 1983 .
[4] J. Cheeger. A lower bound for the smallest eigenvalue of the Laplacian , 1969 .
[5] J. Dodziuk. Difference equations, isoperimetric inequality and transience of certain random walks , 1984 .