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 534
Regular n-tournaments that are not (n − 1)-spectrally monomorphic
Mohamed Zouagui, Abderrahim Boussairi, Imane Souktani, Imane Talbaoui
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
February 18, 2022
March 03, 2435
April 15, 2435

Abstract: The aim of this presentation is to show that there are an infinitely many regular n-tournaments that are not (n−1)-spectrally monomorphic. The smallest example has 7 vertices. To obtain an infinite family of counter-examples, we use the following construction. Let T1, T2 and T3 be three regular n-tournaments with disjoint vertex sets V1 = {v1, . . . ,vn}, V2 = { vn+1, . . . , v2n} and V3 = { v2n+1, . . . , v3n} respectively. Consider the 3n-tournament T with vertex set V = V1 ∪ V2 ∪ V3, obtained from T1, T2 and T3 by adding arcs from V1 to V2, V2 to V3 and V3 to V1. Then, ...