Integral trees with given nullity
Combinatorics
2015-04-24 v2
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.
Keywords
Cite
@article{arxiv.1207.1802,
title = {Integral trees with given nullity},
author = {E. Ghorbani and A. Mohammadian and B. Tayfeh-Rezaie},
journal= {arXiv preprint arXiv:1207.1802},
year = {2015}
}
Comments
14 pages, 4 figures; This is a through revision of the first version including the correction of Lemma 13 (of first version) which was not correct as stated. We thank a referee for pointing out this mistake