Elsevier

Discrete Mathematics

Volume 339, Issue 1, 6 January 2016, Pages 157-164
Discrete Mathematics

Integral trees with given nullity

https://doi.org/10.1016/j.disc.2015.08.007Get rights and content
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Abstract

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.

Keywords

Adjacency eigenvalue
Eigenvalue multiplicity
Nullity
Integral tree

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