On unimodular tournaments

On unimodular tournaments

A tournament is unimodular if the determinant of its skew-adjacency matrix is 1. In this paper, we give some properties and constructions of unimodular tournaments. A unimodular tournament T with skew-adjacency matrix S is invertible if S−1 is the skew-adjacency matrix of a tournament. A spectral ch...

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Veröffentlicht in:Linear algebra and its applications 2022-01, Vol.632, p.50-60
Hauptverfasser: Belkouche, Wiam, Boussaïri, Abderrahim, Chaïchaâ, Abdelhak, Lakhlifi, Soufiane
Format: Artikel
Sprache:eng
Schlagworte:
Apexes
Graphs
Invertible tournament
Linear algebra
Skew-adjacency matrix
Skew-spectra
Tournaments & championships
Unimodular tournament
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Zusammenfassung:A tournament is unimodular if the determinant of its skew-adjacency matrix is 1. In this paper, we give some properties and constructions of unimodular tournaments. A unimodular tournament T with skew-adjacency matrix S is invertible if S−1 is the skew-adjacency matrix of a tournament. A spectral characterization of invertible tournaments is given. Lastly, we show that every n-tournament can be embedded in a unimodular tournament by adding at most n−⌊log2⁡(n)⌋ vertices.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2021.09.014