dc.creator ROJO,OSCAR dc.date 2004-08-01 dc.date.accessioned 2019-11-14T12:58:34Z dc.date.available 2019-11-14T12:58:34Z dc.identifier https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172004000200006 dc.identifier.uri https://revistaschilenas.uchile.cl/handle/2250/118961 dc.description Let p > 1 be an integer. We consider an unweighted balanced tree Bp k of k levels with a root vertex of degree 2p, vertices from the level 2 until the level (k - 1) of degree 2p +1 and vertices in the level k of degree 1. The case p = 1 it was studied in [8, 9, 10]. We prove that the spectrum of the Laplacian matrix L (Bp k) is σ (L (Bp k)) = Uk j =1σ (T(p) j where, for 1< j < k < 1, T(p)j is the j ×j principal submatrix of the tridiagonal k×k singular matrix T(p)k , scanear fórmula We derive that the multiplicity of each eigenvalue of Tj , as an eigenvalue of L (Bp k) , is at least 2(2p-1)2(k-j-1)p . Moreover, we show that the multiplicity of the eigenvalue λ = 1 of L (Bp k) is exactly 2(2p-1)2(k-2)p. Finally, we prove that 3, 7 σ (L (B²k)) if and only if k is a multiple of 3, that 5 σ (L (B2k) if and only if k is an even number, and that no others integer eigenvalues exist for L (B²k). dc.format text/html dc.language en dc.publisher Universidad Católica del Norte, Departamento de Matemáticas dc.relation 10.4067/S0716-09172004000200006 dc.rights info:eu-repo/semantics/openAccess dc.source Proyecciones (Antofagasta) v.23 n.2 2004 dc.subject Tree dc.subject balanced tree dc.subject binary tree dc.subject n-ary tree dc.subject Laplacian matrix dc.title THE SPECTRUM OF THE LAPLACIAN MATRIX OF A BALANCED 2p-ARY TREE
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