Signed graphs with exactly two main eigenvalues: The unicyclic case
Combinatorics
2026-03-05 v1
Abstract
An eigenvalue of a signed graph of order is called a main eigenvalue if its eigenspace is not orthogonal to the all-ones vector . Characterizing signed graphs with exactly distinct main eigenvalues is a problem in algebraic and graph theory that has been studied since 2020. Du et al. (2024, 2026) characterized a class of signed graphs with exactly two main eigenvalues by analyzing a type of multigraph whose base graph is a tree. In this paper, we extend this study to the case where the associated multigraph has a unicyclic base graph, and we conclude by proposing several open problems.
Cite
@article{arxiv.2603.04063,
title = {Signed graphs with exactly two main eigenvalues: The unicyclic case},
author = {Zenan Du and Fenjin Liu and Hechao Liu and Jifu Lin and Wenxu Yang},
journal= {arXiv preprint arXiv:2603.04063},
year = {2026}
}