Star complementary characterization of oriented graphs whose skew spectral radius does not exceed 2
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.
Fields of Study & Subjects
Graph theory and applications
Matrix Theory and Algorithms
Finite Group Theory Research
Publication details
- Journal / source
- Notes on Number Theory and Discrete Mathematics
- Volume
- 32
- Issue
- 1
- Pages
- 120–132
- Publication date
- 26 February 2026
- Language
- EN