Sharp upper and lower bounds for the spectral radius of a nonnegative irreducible matrix and its applications |
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| Authors: | Lihua You Yujie Shu |
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| Institution: | School of Mathematical Sciences, South China Normal University, Guangzhou, P.R. China. |
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| Abstract: | In this paper, we obtain the sharp upper and lower bounds for the spectral radius of a nonnegative irreducible matrix. We also apply these bounds to various matrices associated with a graph or a digraph, obtain some new results or known results about various spectral radii, including the adjacency spectral radius, the signless Laplacian spectral radius, the distance spectral radius, the distance signless Laplacian spectral radius of a graph or a digraph. |
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| Keywords: | Nonnegative matrix irreducible graph digraph spectral radius bound |
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