Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/4231
 Title: Spectra of weighted rooted graphs having prescribed subgraphs at some levels Author: Rojo, O.Robbiano, M.Cardoso, D. M.Martins, E. A. Keywords: Adjacency matrixGeneralized bethe treeLaplacian matrixSignless laplacian matrixWeighted graph Issue Date: 2011 Publisher: ILAS - International Linear Algebra Society Abstract: 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 Δ \subset {1, 2,., k-1} and F={Gj:j \in Δ}, 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 degrees of the vertices, the weights of the edges, and the eigenvalues of the matrices associated to the family of graphs F. These results are applied to characterize the eigenvalues of the Laplacian matrix, including their multiplicities, of the graph β(F) obtained from β and all the graphs in F={Gj:j \in Δ}; and also of the signless Laplacian and adjacency matrices whenever the graphs of the family F are regular. Peer review: yes URI: http://hdl.handle.net/10773/4231 ISSN: 1081-3810 Publisher Version: http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol22_pp653-671.pdf Appears in Collections: DMat - Artigos

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