Abstract
Let P be the set of all primitive (0, 1) matrices of order n, and let D(n, d)≔ {A|A ∈ P and trace(A) = d} . Let E( n, d) be the exponent set of D ( n, d), and let E( n) = ∪ n d=0 E( n, d). It is known that E( n, n) = {1,2,…, n − 1} and E( n, d) = {2,3,…,2 n − d − 1}, 1 ⩽ d ⩽ n − 1. In this note, we prove that E(n, 0) = ∅, n = 1,2, E(n)⧹{1,3}, n = 3, E(n)⧹{1} n ⩾ 4 .
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