Abstract

"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