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 428
Generalized tournaments matrices with the same principal minors
Brahim Chergui, Abderrahim Boussairi, Abdelhak Chaichaa, Soufiane Lakhlifi
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 31, 2022
March 03, 2361
April 15, 2361

Abstract: Let T be a tournament, that is, an orientation of the complete graph, and let A be its adjacency matrix. A subset X of the vertex set V is called a clan, if for every z ∈ V \ X, the arcs between X and z have the same direction. Bousaïri et al. [5] proved that two tournaments have the same 3-cycles iff one is obtained from the other by a sequence of clan reversals. Matricially, this result result can be stated as follows: two tournament matrices have the same principal minors of order 3 iff they are related by a sequence of clan reversals. A generalized tournament matrix M is a ...