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

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Some spectral properties of starlike trees

M. Lepovic and I. Gutman

Faculty of Science, University of Kragujevac, P.O.Box 60, YU-34000 Kragujevac, Yugoslavia

Abstract: 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 $\sqrt{k} \leq \lambda_1 < k/\sqrt{k-1}$ . 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

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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
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