Integral trees of arbitrarily large diameters

  • Authors:

  • Péter Csikvári

  • Affiliations:

  • Department of Computer Science, Eötvös Loránd University, Budapest, Hungary 1117

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 2010

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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|.