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

Spectra of copies of Bethe trees attached to path and applicationsMaria Robbiano, I. Gutman, R. Jiménez and B. San martinUniversidad Catolica del Norte, Universidad de Antofagasta, Antofagasta, ChileFaculty 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 $k1$ 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 Full text of the article: (for faster download, first choose a mirror)
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