Acyclic digraphs and eigenvalues of -matrices.

McKay, Brendan D.; Oggier, Frédérique E.; Royle, Gordon F.; Sloane, N.J.A.; Wanless, Ian M.; Wilf, Herbert S.

Displaying similar documents to “Acyclic digraphs and eigenvalues of $(0, 1)$ -matrices.”

Limit points of eigenvalues of (di)graphs

Fu Ji Zhang, Zhibo Chen (2006)

Czechoslovak Mathematical Journal

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The study on limit points of eigenvalues of undirected graphs was initiated by A. J. Hoffman in 1972. Now we extend the study to digraphs. We prove: 1. Every real number is a limit point of eigenvalues of graphs. Every complex number is a limit point of eigenvalues of digraphs. 2. For a digraph $D$ , the set of limit points of eigenvalues of iterated subdivision digraphs of $D$ is the unit circle in the complex plane if and only if $D$ has a directed cycle. 3. Every limit point of eigenvalues...

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). ...