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Hall exponents of matrices, tournaments and their line digraphs

Richard A. Brualdi; Kathleen P. Kiernan — 2011

Czechoslovak Mathematical Journal

Let $A$ be a square $(0, 1)$ -matrix. Then $A$ is a Hall matrix provided it has a nonzero permanent. The Hall exponent of $A$ is the smallest positive integer $k$ , if such exists, such that $A^{k}$ is a Hall matrix. The Hall exponent has received considerable attention, and we both review and expand on some of its properties. Viewing $A$ as the adjacency matrix of a digraph, we prove several properties of the Hall exponents of line digraphs with some emphasis on line digraphs of tournament (matrices).

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