Spectral Slater index of tournaments

Main Article Content

Abderrahim Boussaïri
Abdelhak Chaïchaâ
Brahim Chergui
https://orcid.org/0000-0002-6909-5760
Sara Ezzahir
Soufiane Lakhlifi
https://orcid.org/0000-0002-9923-4493
Soukaïna Mahzoum

Abstract

The Slater index $i(T)$ of a tournament $T$ is the minimum number of arcs that must be reversed to make $T$ transitive. In this paper, we define a parameter $\Lambda(T)$ from the spectrum of the skew-adjacency matrix of $T$, called the spectral Slater index. This parameter is a measure of remoteness between the spectrum of $T$ and that of a transitive tournament. We show that $\Lambda(T)\leq8\, i(T)$ and we characterize the tournaments with maximal spectral Slater index. As an application, an improved lower bound on the Slater index of doubly regular tournaments is given.

Article Details

Section
Article