Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4646808 | Discrete Mathematics | 2016 | 8 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
E. Ghorbani, A. Mohammadian, B. Tayfeh-Rezaie,