Integral trees with given nullity

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.

• Type: Journal
• Year: 2016
• Where: DM
• Keywords: DM 2016