Geodesic
A result related to the largest eigenvalue of a tree
Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 3, pp. 557-561.

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In this note we prove that 0,1,√2,√3,2 is the set of all real numbers l such that the following holds: every tree having an eigenvalue which is larger than l has a subtree whose largest eigenvalue is l.
Keywords: eigenvalues of a graph, characteristic polynomial 
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Vijayakumar, Gurusamy. A result related to the largest eigenvalue of a tree. Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 3, pp. 557-561. http://geodesic.mathdoc.fr/item/DMGT_2008_28_3_a13/

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