Geodesic
Some spectral properties of starlike trees
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 26 (2001), p. 107 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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.
Classification : 05C05 05C50
Keywords: Starlike trees, Spectra (of graphs), Hyperbolic graphs, Integral graphs 
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     author = {M. Lepovi\'c and I. Gutman},
     title = {Some spectral properties of starlike trees},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {107 },
     year = {2001},
     volume = {26},
     zbl = {0997.05059},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASS_2001_26_a5/}
}
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M. Lepović; I. Gutman. Some spectral properties of starlike trees. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 26 (2001), p. 107 . http://geodesic.mathdoc.fr/item/BASS_2001_26_a5/