Locating Eigenvalues of Perturbed Laplacian Matrices of Trees
ABSTRACT We give a linear time algorithm to compute the number of eigenvalues of any perturbed Laplacian matrix of a tree in a given real interval. The algorithm can be applied to weighted or unweighted trees. Using our method we characterize the trees that have up to 5 distinct eigenvalues with respect to a family of perturbed Laplacian matrices that includes the adjacency and normalized Laplacian matrices as special cases, among others.
Saved in:
Main Authors: | , |
---|---|
Format: | Digital revista |
Language: | English |
Published: |
Sociedade Brasileira de Matemática Aplicada e Computacional
2017
|
Online Access: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512017000300479 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Summary: | ABSTRACT We give a linear time algorithm to compute the number of eigenvalues of any perturbed Laplacian matrix of a tree in a given real interval. The algorithm can be applied to weighted or unweighted trees. Using our method we characterize the trees that have up to 5 distinct eigenvalues with respect to a family of perturbed Laplacian matrices that includes the adjacency and normalized Laplacian matrices as special cases, among others. |
---|