Hermitian adjacency matrices with at most three distinct eigenvalues
Combinatorics
2025-12-08 v2
Abstract
We study oriented graphs whose Hermitian adjacency matrices of the second kind have few eigenvalues. We give a complete characterization of the oriented graphs with two distinct eigenvalues, showing that there are only four such graphs. We extend this result to mixed graphs. We show that there are infinitely many regular tournaments with three distinct eigenvalues. We extend our main results to Hermitian adjacency matrices defined over other roots of unity.
Keywords
Cite
@article{arxiv.2503.13781,
title = {Hermitian adjacency matrices with at most three distinct eigenvalues},
author = {Saieed Akbari and Jonathan Aloni and Maxwell Levit and Bojan Mohar and Steven Xia},
journal= {arXiv preprint arXiv:2503.13781},
year = {2025}
}
Comments
18 pages, Journal version, includes extension of main theorem to mixed graphs