The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

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

Similarity:

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

Similarity:

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). ...