Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
31 January 2020 |
15 February 2020 |
10 March 2020 |
Abstract: Let T = (V,A) be a tournament on n vertices. The adjacency matrix of the tournament T is the n×n matrix A = (a_ij) in which a_ij=1 if (v_i,v_j) =1 and 0 otherwhise. A (0,1)-tournament is a tournament related to its adjacency matrix A such that A + A^t = J-I, where I and J will (respectively) denote the n×n identity matrix and all-ones matrix. We say that a (0,1)-tournament is (n-2)- monomorphic if all its principal submatrices of order n-2 are isomorphic. Moreover, we say that it is (n-2)- spectrally monomorphic if all its principal submatrices of order n-2 have the same characteristic polynomials. In the present paper, we give a characterization of (n-2)-spectrally monomorphic (0,1)-tournaments.
