| dc.creator | ROJO,OSCAR | |
| dc.date | 2004-08-01 | |
| dc.date.accessioned | 2020-02-17T15:32:53Z | |
| dc.date.available | 2020-02-17T15:32:53Z | |
| dc.identifier | https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172004000200006 | |
| dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/130457 | |
| 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 <IMG SRC="/fbpe/img/proy/v23n2/e.jpg" WIDTH=18 HEIGHT=16>σ (L (B²k)) if and only if k is a multiple of 3, that 5 <IMG SRC="/fbpe/img/proy/v23n2/e.jpg" WIDTH=18 HEIGHT=16>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 | |
