English

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.

Keywords

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}
}
R2 v1 2026-06-21T19:13:47.198Z