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.
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| Main Authors: | , |
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| Format: | Digital revista |
| Language: | English |
| Published: |
Sociedade Brasileira de Matemática Aplicada e Computacional
2017
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| Online Access: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512017000300479 |
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