Open AccessSpectral Slater index of tournaments
Author(s) -
Abderrahim Boussaïri,
Abdelhak Chaïchaâ,
Brahim Chergui,
Sara Ezzahir,
Soufiane Lakhlifi,
Soukaïna Mahzoum
Publication year - 2022
Publication title -
the electronic journal of linear algebra
Language(s) - English
Resource type - Journals
eISSN - 1537-9582
pISSN - 1081-3810
DOI - 10.13001/ela.2022.6407
Subject(s) - mathematics , tournament , transitive relation , combinatorics , index (typography) , adjacency matrix , measure (data warehouse) , matrix (chemical analysis) , discrete mathematics , graph , computer science , materials science , database , world wide web , composite material
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.