Computing the Laplacian spectra of some graphs

Authors:
Domingos M. Cardoso;Enide Andrade Martins;MaríA Robbiano;Vilmar Trevisan
Affiliations:
Departamento de Matemática, Universidade de Aveiro, 3810-193 Aveiro, Portugal;Departamento de Matemática, Universidade de Aveiro, 3810-193 Aveiro, Portugal;Departamento de Matemáticas, Universidad Católica del Norte, Antofagasta, Chile;Instituto de Matemática, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brazil
Venue:
Discrete Applied Mathematics
Year:
2012

Citing 3
Cited 0

The Laplacian spectrum of a graph

SIAM Journal on Matrix Analysis and Applications
The Laplacian Spectrum of a Graph II

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Applied numerical linear algebra

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Abstract

In this paper we give a simple characterization of the Laplacian spectra of a family of graphs as the eigenvalues of symmetric tridiagonal matrices. In addition, we apply our result to obtain upper and lower bounds for the Laplacian-energy-like invariant of these graphs. The class of graphs considered are obtained from copies of modified generalized Bethe trees (obtained by joining the vertices at some level by paths), identifying their roots with the vertices of a regular graph or a path.