Integral trees with given nullity
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. It is also shown that integral trees with nullity 2 and 3 are unique.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2012
- DOI:
- 10.48550/arXiv.1207.1802
- arXiv:
- arXiv:1207.1802
- Bibcode:
- 2012arXiv1207.1802G
- Keywords:
-
- Mathematics - Combinatorics;
- 05C50;
- 05C05;
- 15A18
- E-Print:
- 14 pages, 4 figures