The Spectrum and Eigenvectors of the Laplacian Matrices of the Brualdi-Li Tournament Digraphs

Abstract

Let $m\ge \mathrm{1}$ be an integer, let ${ℬ}_{\mathrm{2}m}$ denote the Brualdi-Li matrix of order $\mathrm{2}m$, and let $ℒ{ℬ}_{\mathrm{2}m}$ denote the Laplacian matrices of Brualdi-Li tournament digraphs. We obtain the eigenvalues and eigenvectors of $ℒ{ℬ}_{\mathrm{2}m}$.