Locating Eigenvalues of a Symmetric Matrix whose Graph is Unicyclic

Authors

  • R. O. Braga Departamento de Matemática Pura e Aplicada, IME- Instituto de Matemática e Estatística UFRGS - Universidade Federal do Rio Grande do Sul https://orcid.org/0000-0002-6156-2213
  • V. M. Rodrigues Departamento de Matemática Pura e Aplicada, IME- Instituto de Matemática e Estatística UFRGS - Universidade Federal do Rio Grande do Sul https://orcid.org/0000-0002-1964-3327
  • R. O. Silva Departamento de Matemática Pura e Aplicada, IME- Instituto de Matemática e Estatística UFRGS - Universidade Federal do Rio Grande do Sul

DOI:

https://doi.org/10.5540/tcam.2021.022.04.00659

Keywords:

Symmetric matrix, eigenvalue location, unicyclic graph.

Abstract

We present a linear-time algorithm that computes in a given real interval the number of eigenvalues of any symmetric matrix whose underlying graph is unicyclic. The algorithm can be applied to vertex- and/or edge-weighted or unweighted unicyclic graphs. We apply the algorithm to obtain some general results on the spectrum of a generalized sun graph for certain matrix representations which include the Laplacian, normalized Laplacian and signless Laplacian matrices.

Author Biography

R. O. Braga, Departamento de Matemática Pura e Aplicada, IME- Instituto de Matemática e Estatística UFRGS - Universidade Federal do Rio Grande do Sul

Doutor em Matemática Aplicada (UFRGS, 2015)

References

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R. O. Braga, V. M. Rodrigues, and V. Trevisan. Locating eigenvalues of unicyclicgraphs.Appl. Anal. Discrete Math., 11(2):273–298, 2017.

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Published

2021-10-26

How to Cite

Braga, R. O., Rodrigues, V. M., & Silva, R. O. (2021). Locating Eigenvalues of a Symmetric Matrix whose Graph is Unicyclic. Trends in Computational and Applied Mathematics, 22(4), 659–674. https://doi.org/10.5540/tcam.2021.022.04.00659

Issue

Vol. 22 No. 4 (2021)

Section

Original Article

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