Hermitian adjacency matrices with at most three distinct eigenvalues

Akbari, Saieed (author), Aloni, Jonathan (author), Levit, Maxwell (author), Mohar, Bojan (author), Xia, Steven (author)

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.

• Language: English
• Keywords: Hermitian adjacency matrix, few distinct eigenvalues, oriented graphs, mixed graphs
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.03.2026
• Year: 2026
• Number of pages: 11 str.
• Numbering: Vol. 349, iss. 3, art. no. 114872
• PID: 20.500.12556/RUL-176452
• UDC: 519.17:512
• ISSN on article: 0012-365X
• DOI: 10.1016/j.disc.2025.114872
• COBISS.SI-ID: 259134723
• Publication date in RUL: 01.12.2025

Record is a part of a journal

• Title: Discrete mathematics
• Shortened title: Discrete math.
• Publisher: Elsevier
• ISSN: 0012-365X
• COBISS.SI-ID: 1118479

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• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
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