Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 487
On invertible tournaments
Wiam Belkouche, Abderrahim Boussaïri, Abdelhak Chaïchaâ, Soufiane Lakhlifi
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
February 01, 2022
March 03, 2403
April 15, 2403

Abstract: We say that a tournament T is invertible if the inverse of its skew-adjacency matrix is a skew-adjacency matrix of a tournament. This tournament is said to be the inverse of T. Invertible tournaments are inherently unimodular, that is the determinant of their skew-adjacency matrices is equal to 1. Moreover, its principal minors are necessarily subject to some conditions. In this talk, we give a characterization of invertible tournaments and present some families of such tournaments.