Abstract
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|.
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To the memory of Gács András.
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Csikvári, P. Integral trees of arbitrarily large diameters. J Algebr Comb 32, 371–377 (2010). https://doi.org/10.1007/s10801-010-0218-8
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DOI: https://doi.org/10.1007/s10801-010-0218-8