Nonderogatory directed windmills.

Rada, Juán

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On digraphs with non-derogatory adjacency matrix.

Deng, C.L., Gan, C.S. (1998)

Bulletin of the Malaysian Mathematical Society. Second Series

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The complete product of annihilatingly unique digraphs.

Gan, C.S. (2005)

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Hall exponents of matrices, tournaments and their line digraphs

Richard A. Brualdi, Kathleen P. Kiernan (2011)

Czechoslovak Mathematical Journal

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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). ...