On unimodular tournaments

Wiam Belkouche, Abderrahim Boussaïri, Abdelhak Chaïchaâ, Soufiane Lakhlifi
2021 Linear Algebra and its Applications  
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 - ⌊log_2(n)⌋ vertices.
doi:10.1016/j.laa.2021.09.014 fatcat:2t6lnpber5hr3dtkxlpupf6yc4