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Eigenvalue bounds for some classes of matrices associated with graphs
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 1, pp. 231-251
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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 the 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 and the largest eigenvalues of the Laplacian matrices of graphs. The sharpness of these bounds is verified by examples.
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 the 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 and the largest eigenvalues of the Laplacian matrices of graphs. The sharpness of these bounds is verified by examples.
DOI : 10.21136/CMJ.2020.0290-19
Classification : 05C50
Keywords: adjacency matrix; Laplacian matrix; normalized adjacency matrix; spectral radius; algebraic connectivity; Randić index 
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Mehatari, Ranjit; Kannan, M. Rajesh. Eigenvalue bounds for some classes of matrices associated with graphs. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 1, pp. 231-251. doi: 10.21136/CMJ.2020.0290-19

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