Eigenvalue bounds for some classes of matrices associated with graphs

Ranjit Mehatari; M. Rajesh Kannan

Czechoslovak Mathematical Journal (2021)

  • Issue: 1, page 231-251
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Mehatari, Ranjit, and Kannan, M. Rajesh. "Eigenvalue bounds for some classes of matrices associated with graphs." Czechoslovak Mathematical Journal (2021): 231-251. <http://eudml.org/doc/297249>.

@article{Mehatari2021,
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 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.},
author = {Mehatari, Ranjit, Kannan, M. Rajesh},
journal = {Czechoslovak Mathematical Journal},
keywords = {adjacency matrix; Laplacian matrix; normalized adjacency matrix; spectral radius; algebraic connectivity; Randić index},
language = {eng},
number = {1},
pages = {231-251},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Eigenvalue bounds for some classes of matrices associated with graphs},
url = {http://eudml.org/doc/297249},
year = {2021},
}

TY - JOUR
AU - Mehatari, Ranjit
AU - Kannan, M. Rajesh
TI - Eigenvalue bounds for some classes of matrices associated with graphs
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 231
EP - 251
AB - 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.
LA - eng
KW - adjacency matrix; Laplacian matrix; normalized adjacency matrix; spectral radius; algebraic connectivity; Randić index
UR - http://eudml.org/doc/297249
ER -

References

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