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.
Publisher
Brazilian Society for Computational and Applied Mathematics (SBMAC)
Cited by
2 articles.
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1. Diminimal families of arbitrary diameter;Linear Algebra and its Applications;2023-11
2. Locating Eigenvalues in Trees;Locating Eigenvalues in Graphs;2022