Isospectral graphs with identical nodal counts
Mathematical Physics
2016-11-25 v1 math.MP
Abstract
According to a recent conjecture, isospectral objects have different nodal count sequences. We study generalized Laplacians on discrete graphs, and use them to construct the first non-trivial counter-examples to this conjecture. In addition, these examples demonstrate a surprising connection between isospectral discrete and quantum graphs.
Cite
@article{arxiv.1110.0158,
title = {Isospectral graphs with identical nodal counts},
author = {Idan Oren and Ram Band},
journal= {arXiv preprint arXiv:1110.0158},
year = {2016}
}