Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques Vol. CXXII, No. 26, pp. 107–113 (2001) 

Some spectral properties of starlike treesM. Lepovic and I. GutmanFaculty of Science, University of Kragujevac, P.O.Box 60, YU34000 Kragujevac, YugoslaviaAbstract: A tree is said to be starlike if exactly one of its vertices has degree greater than two. We show that almost all starlike trees are hyperbolic, and determine all exceptions. If $k$ is the maximal vertex degree of a starlike tree and $\lambda_1$ is its largest eigenvalue, then $\sqrt{k} \leq \lambda_1 < k/\sqrt{k1}$ . A new way to characterize integral starlike trees is put forward. Keywords: Starlike trees, Spectra (of graphs), Hyperbolic graphs, Integral graphs Classification (MSC2000): 05C05, 05C50 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 20 Aug 2001. This page was last modified: 20 Jun 2011.
© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
