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Bibliographic Details
Main Authors: Du, Zenan, Liu, Fenjin, Liu, Hechao, Lin, Jifu, Yang, Wenxu
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2603.04063
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Table of Contents:
  • An eigenvalue $λ$ of a signed graph $S$ of order $n$ is called a main eigenvalue if its eigenspace is not orthogonal to the all-ones vector $j$. Characterizing signed graphs with exactly $k$ $(1\le k\le n)$ 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.