EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques
Vol. CXXXVII, No. 33, pp. 59–81 ()

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Spectra of copies of Bethe trees attached to path and applications

Maria Robbiano, I. Gutman, R. Jiménez and B. San martin

Universidad Catolica del Norte, Universidad de Antofagasta, Antofagasta, Chile
Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia

Abstract: The Bethe tree $B_{d,k}$ is the rooted tree of $k$ levels whose root vertex has degree $d$ , the vertices from level 2 to level $k-1$ have degree $d+1$ , and the vertices at level $k$ have degree 1. This paper gives a decomposition of the characteristic polynomial of the adjacency matrix of the tree $T(d,k,r)$ , obtained by attaching copies of $B(d,k)$ to the vertices of the $r$-vertex path. Moreover, lower and upper bounds for the energy of $T(d,k,r)$ are obtained.

Keywords: spectrum (of graph), energy (of graph), Bethe tree

Classification (MSC2000): 05C50

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Electronic fulltext finalized on: 7 Sep 2008. This page was last modified: 20 Jun 2011.

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