Acyclic Digraphs and Eigenvalues of O,1 Matrices

McKay, Brendan; Oggier, Frederique; Royle, Gordon; Sloane, N J A; Wanless, Ian; Wilf, Herbert

Acyclic Digraphs and Eigenvalues of O,1 Matrices

Date

2004

Authors

McKay, Brendan

Oggier, Frederique

Royle, Gordon

Sloane, N J A

Wanless, Ian

Wilf, Herbert

Publisher

University of Waterloo

Abstract

We show that the number of acyclic directed graphs with n labeled vertices is equal to the number of n × n (0, 1)-matrices whose eigenvalues are positive real numbers.

Keywords

Keywords: Asymptotic stability; Eigenvalues and eigenfunctions; Matrix algebra; Number theory; Problem solving; Theorem proving; Acyclic digraphs; Arithmetic means; Geometric means; Permutation matrices; Graph theory (0, 1)-matrix; Acyclic; Digraph; Eigenvalue

URI

http://hdl.handle.net/1885/82870

Collections

ANU Research Publications

Source

Journal of Integer Sequences

Type

Journal article

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Acyclic Digraphs and Eigenvalues of O,1 Matrices

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