# Spectra of weighted rooted graphs having prescribed subgraphs at some levels

@inproceedings{Rojo2011SpectraOW, title={Spectra of weighted rooted graphs having prescribed subgraphs at some levels}, author={Oscar Rojo and Mar{\'i}a Robbiano and Domingos M. Cardoso and Enide Andrade Martins}, year={2011} }

- Published 2011
DOI:10.13001/1081-3810.1465

Let B be a weighted generalized Bethe tree of k levels (k > 1) in which nj is the number of vertices at the level k− j +1 (1 ≤ j ≤ k). Let ∆ ⊆ {1, 2, . . . , k − 1} and F= {Gj : j ∈ ∆}, where Gj is a prescribed weighted graph on each set of children of B at the level k−j+1. In this paper, the eigenvalues of a block symmetric tridiagonal matrix of order n1 +n2 + · · ·+nk are characterized as the eigenvalues of symmetric tridiagonal matrices of order j, 1 ≤ j ≤ k, easily constructed from the… CONTINUE READING