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Paper   IPM / M / 14000
School of Mathematics
  Title:   Integral trees with given nullity
1.  E. Ghorbani
2.  A. Mohammadian
3.  B. Tayfeh-Rezaie
  Status:   Published
  Journal: Discrete Mathematics
  Vol.:  339
  Year:  2016
  Pages:   157-164
  Editor:  157-164
  Supported by:  IPM
A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. We prove that for a given nullity more than 1, there are only finitely many integral trees. Integral trees with nullity at most 1 were already characterized by Watanabe and Brouwer. It is shown that integral trees with nullity 2 and 3 are unique.

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