Abstract
We prove that the exponent set of symmetric primitive (0, 1) matrices with zero trace (the adjacency matrices of the simple graphs) is {2,3,…,2 n−4}⧹ S, where S is the set of all odd numbers in { n−2, n−1,…,2 n−5}. We also obtain a characterization of the symmetric primitive matrices with zero trace whose exponents attain the upper bound 2 n−4.
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