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

^*Corresponding author for this work

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

30 Citations (Scopus)

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 - 2004

Cite this

@article{e82534b562f54d3cbe75f726ffb8381e,

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.\}",

year = "2004",

language = "English",

volume = "7",

journal = "Journal of Integer Sequences",

issn = "1530-7638",

publisher = "University of Waterloo",

number = "3",

}

TY - JOUR

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

Y1 - 2004

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 - https://www.scopus.com/pages/publications/4644250101

M3 - Article

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

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