Locating Eigenvalues of a Symmetric Matrix whose Graph is Unicyclic
DOI:
https://doi.org/10.5540/tcam.2021.022.04.00659Keywords:
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.References
F. Belardo, M. Brunetti, and V. Trevisan. Locating eigenvalues of unbalancedunicyclic signed graphs.Appl. Math. Comput., 400:126082, 2021.
R. O. Braga, R. R. Del-Vecchio, and V. M. Rodrigues. Integral unicyclic graphs.Linear Algebra Appl., 614:281–300, 2021.
R. O. Braga and V. M. Rodrigues. Locating eigenvalues of perturbed Laplacianmatrices of trees.TEMA Tend. Mat. Apl. Comput., 18(3):479–491, 2017.
R. O. Braga, V. M. Rodrigues, and V. Trevisan. Locating eigenvalues of unicyclicgraphs.Appl. Anal. Discrete Math., 11(2):273–298, 2017.
F. R. K. Chung.Spectral Graph Theory. American Mathematical Society, 1997.
P. J. Davis.Circulant matrices. John Wiley & Sons, New York-Chichester-Brisbane, 1979. A Wiley-Interscience Publication, Pure and Applied Mathe-matics.
D. P. Jacobs and V. Trevisan. Locating the eigenvalues of trees.Linear AlgebraAppl., 434(1):81–88, 2011.
R. Merris. Laplacian matrices of graphs: a survey. volume 197/198, pages143–176. 1994. Second Conference of the International Linear Algebra Society(ILAS) (Lisbon, 1992)
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