On Some Properties for the Sequence of Brualdi-Li Matrices

Abstract

LetB2ndenote the Brualdi-Li matrix, and letρ2n=ρ(B2n)denote the Perron value of the Brualdi-Li matrix of order2n. We prove that2n(n-1/2-ρ2n)is monotonically decreasing for allnandρ2n<n-1/2-(e2-1)/4(e2+1)n, wheree=2.718281828459045….

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

“…This conjecture has been confirmed in [8]. The properties of the Brualdi-Li matrix have been investigated in [9][10][11][12][13][14].…”