Locating Eigenvalues of Perturbed Laplacian Matrices of Trees

Rodrigo Orsini Braga, Virgínia Maria Rodrigues

Abstract


We give a linear time algorithm to compute the number of eigenvalues of any perturbedLaplacian matrix of a tree in a given real interval. The algorithm can be applied to weightedor unweighted trees. Using our method we characterize the trees that have up to $5$ distincteigenvalues with respect to a family of perturbed Laplacian matrices that includes the adjacencyand normalized Laplacian matrices as special cases, among others.

Keywords


Perturbed Laplacian matrix, eigenvalue location, trees

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References


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DOI: http://dx.doi.org/10.5540/tema.2017.018.03.479

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TEMA - Trends in Applied and Computational Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
ISSN: 1677-1966  (print version),  2179-8451  (online version)

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