Abstract
A tournament is k-spectrally monomorphic if all the k×k principal submatrices of its adjacency matrix have the same characteristic polynomial. Transitive n-tournaments are trivially k-spectrally monomorphic. We show that there are no others for k∈{3,…,n−3}. Furthermore, we prove that for n≥5, a non-transitive n-tournament is (n−2)-spectrally monomorphic if and only if it is doubly regular. Finally, we give some results on (n−1)-spectrally monomorphic regular tournaments.
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