Locating Eigenvalues of Perturbed Laplacian Matrices of Trees
TEMA (São Carlos)(2018)
摘要
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.
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关键词
Eigenvalue Problems,Eigenvalues,Matrix Computations
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