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}
}
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

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