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|Paper IPM / M / 14000||
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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