Geodesic
Integral trees of arbitrarily large diameters
Journal of Algebraic Combinatorics, Tome 32 (2010) no. 3, pp. 371-377.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper, we construct trees having only integer eigenvalues with arbitrarily large diameters. In fact, we prove that for every finite set $S$ of positive integers there exists a tree whose positive eigenvalues are exactly the elements of $S$. If the set $S$ is different from the set 1 then the constructed tree will have diameter $2| S|$.
Keywords: keywords trees, eigenvalues 
@article{JAC_2010__32_3_a5,
     author = {Csikv\'ari, P\'eter},
     title = {Integral trees of arbitrarily large diameters},
     journal = {Journal of Algebraic Combinatorics},
     pages = {371--377},
     publisher = {mathdoc},
     volume = {32},
     number = {3},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2010__32_3_a5/}
}
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Csikvári, Péter. Integral trees of arbitrarily large diameters. Journal of Algebraic Combinatorics, Tome 32 (2010) no. 3, pp. 371-377. http://geodesic.mathdoc.fr/item/JAC_2010__32_3_a5/