Star complementary characterization of oriented graphs whose skew spectral radius does not exceed 2

Zoran Stanić
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 32, 2026, Number 1, Pages 120–132
DOI: 10.7546/nntdm.2026.32.1.120-132
Full paper (PDF, 300 Kb)

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Authors and affiliations

Zoran Stanić
Faculty of Mathematics, University of Belgrade
Studentski trg 16, Serbia

Abstract

We employ the method of star complements to classify all oriented graphs whose skew spectrum lies within the interval [–2, 2]. At the same time, we provide a structural characterisation of these graphs, showing that, with the sole exception of exactly one graph of order 14, every maximal oriented graph possessing this spectral property is determined by a fixed oriented cycle serving as a star complement for either –2 or 2. The exceptional oriented graph is uniquely determined by a fixed 7-vertex oriented path acting as the star complement. This work may be regarded as a counterpart to [13], where the corresponding oriented graphs were determined via associated signed graphs, without the present characterisation.

Keywords

• Star complement
• Oriented graph
• Skew spectral radius
• Prescribed induced subgraph

2020 Mathematics Subject Classification

• 05C50
• 05C20
• 05C22

References

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Manuscript history

• Received: 10 October 2025
• Revised: 23 February 2026
• Accepted: 25 February 2026
• Online First: 26 February 2026

Copyright information

Ⓒ 2026 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).