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Let A be a primitive matrix of order n, and let k be an integer with 1⩽k⩽n. The kth local exponent of A, is the smallest power of A for which there are k rows with no zero entry. We have recently obtained the maximum value for the kth local exponent of doubly symmetric primitive matrices of order n with 1⩽k⩽n. In this paper, we use the graph theoretical method to give a complete characterization of...
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