Acyclic digraphs and eigenvalues of (0, 1)-matrices

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

Acyclic digraphs and eigenvalues of (0, 1)-matrices

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

Research output: Contribution to journal › Article › Research › peer-review

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.

Original language	English
Journal	Journal of Integer Sequences
Volume	7
Issue number	3
Publication status	Published - 1 Jan 2004
Externally published	Yes

Keywords

(0, 1)-matrix
Acyclic
Digraph
Eigenvalue

Cite this

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title = "Acyclic digraphs and eigenvalues of (0, 1)-matrices",

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 = "(0, 1)-matrix, Acyclic, Digraph, Eigenvalue",

author = "McKay, {Brendan D.} and Oggier, {Pr{\'e}d{\'e}rique E.} and Royle, {Gordon F.} and Sloane, {N. J A} and Wanless, {Ian M.} and Wilf, {Herbert S.}",

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T1 - Acyclic digraphs and eigenvalues of (0, 1)-matrices

AU - McKay, Brendan D.

AU - Oggier, Prédérique E.

AU - Royle, Gordon F.

AU - Sloane, N. J A

AU - Wanless, Ian M.

AU - Wilf, Herbert S.

PY - 2004/1/1

Y1 - 2004/1/1

N2 - 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.

AB - 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.

KW - (0, 1)-matrix

KW - Acyclic

KW - Digraph

KW - Eigenvalue

UR - http://www.scopus.com/inward/record.url?scp=4644250101&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:4644250101

SN - 1530-7638

VL - 7

JO - Journal of Integer Sequences

JF - Journal of Integer Sequences

IS - 3

ER -

Acyclic digraphs and eigenvalues of (0, 1)-matrices

Abstract

Keywords

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Cite this