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Eigenvalue bounds for some classes of matrices associated with graphs
release_dyecq5nborcijhzb7vezbu6nbi
by
Ranjit Mehatari, M. Rajesh Kannan
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as a article
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2020
Abstract
For a given complex square matrix A with constant row sum, we establish two
new eigenvalue inclusion sets. Using these bounds, first we derive bounds for
the second largest and smallest eigenvalues of adjacency matrices of
k-regular graphs. Then, we establish some bounds for the second largest and
the smallest eigenvalues of the normalized adjacency matrices of graphs and the
second smallest eigenvalue and the largest eigenvalue of the Laplacian matrices
of graphs. Sharpness of these bounds are verified by examples.
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1812.04916v2
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