On almost regular tournament matrices

Spectral and determinantal properties of a special dass M-n of 2n x 2n almo st regular tournament matrices are studied. In particular, the maximum Perr on value of the matrices in this class is determined and shown to be achiev ed by the Brualdi-Li matrix, which has been conjectured to have the largest Perron value among all tournament matrices of even order. We also establis h some determinantal inequalities for matrices in M-n and describe the stru cture of their associated walk spaces. (C) 2000 Elsevier Science Inc. All r ights reserved.