A096368 -id:A096368 - cp's OEIS frontend

A219889 Number of directed 2-regular graphs on n nodes.

1, 2, 5, 23, 92, 624, 5021, 47034, 494320, 5719769, 71971687

Offset: 3

N. J. A. Sloane, Nov 30 2012

Gunnar Brinkmann, Generating regular directed graphs, Discrete Math., 313 (2012), 1-7.
R. J. Mathar, OEIS A219889
Richard J. Mathar, 2-regular Digraphs of the Lovelock Lagrangian, arXiv:1903.12477 [math.GM], 2019.

Column k=2 of A350910.

Cf. A096368, A219890, A219891, A219892, A219893, A307155 (connected, inverse Euler Trans.), A007107 (labeled), A306827 (multiedges, connected), A002865 (directed 1-regular unlabeled no loops), A005641 (loops allowed)

A058338 Number of digraphs with indegree = outdegree at each vertex, or Eulerian digraphs (including disconnected graphs) with n nodes.

Original entry on oeis.org

1, 1, 2, 5, 18, 111, 2292, 181519, 51294836, 48814342597, 157166848652408, 1736132851915020181, 66689407510956897981608, 9012860249531358132125181323, 4328664025050045497712238253179872, 7451990930474005836163802713084971814275, 46329549163592383403451764167315165130121820112

Offset: 0

N. J. A. Sloane

Every regular tournament (A096368) is a Eulerian digraph. Similar methods may be used to compute terms of this sequence. - Andrew Howroyd, Apr 12 2020

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 219 (but there is an error).
Ronald C. Read, email to N. J. A. Sloane, 28 August, 2000.

Cf. A007080 (labeled), A058337 (connected), A096368, A308161, A308111.

A058337 = Cases[Import["https://oeis.org/A058337/b058337.txt", "Table"], {, }][[All, 2]];
(* EulerTransform is defined in A005195 *)
EulerTransform[Rest @ A058337] (* Jean-François Alcover, Feb 23 2020, upated Mar 18 2020 *)

Euler transform of A058337.

a(7) added using A058337 by Falk Hüffner, Dec 03 2015
a(8) and a(9) added using A058337 by Brendan McKay, May 05 2019
Terms a(10) and beyond from Andrew Howroyd, Apr 12 2020

A219890 Number of directed 3-regular graphs on n nodes.

Original entry on oeis.org

1, 2, 23, 415, 19041, 1104045, 79818336, 6958257941, 720814138673, 87579097910309

Offset: 4

N. J. A. Sloane, Nov 30 2012

Gunnar Brinkmann, Generating regular directed graphs, Discrete Math., 313 (2012), 1-7.

Column k=3 of A350910.

Cf. A096368, A219889, A219890, A219891, A219892, A219893.

A219891 Number of directed 4-regular graphs on n nodes.

Original entry on oeis.org

1, 4, 92, 19041, 6510087, 2983458766, 1775668832509, 1349509467853512

Offset: 5

N. J. A. Sloane, Nov 30 2012

Gunnar Brinkmann, Generating regular directed graphs, Discrete Math., 313 (2012), 1-7.

Column k=4 of A350910.

Cf. A096368, A219889, A219890, A219892, A219893.

A219892 Number of directed 5-regular graphs on n nodes.

Original entry on oeis.org

1, 4, 624, 1104045, 2983458766, 10922621656743

Offset: 6

N. J. A. Sloane, Nov 30 2012

Gunnar Brinkmann, Generating regular directed graphs, Discrete Math., 313 (2012), 1-7.

Column k=5 of A350910.

Cf. A096368, A219889, A219890, A219891, A219893.

A219893 Number of directed 6-regular graphs on n nodes.

Original entry on oeis.org

1, 7, 5021, 79818336, 1775668832509

Offset: 7

N. J. A. Sloane, Nov 30 2012

Gunnar Brinkmann, Generating regular directed graphs, Discrete Math., 313 (2012), 1-7.

Column k=6 of A350910.

Cf. A096368, A219889, A219890, A219891, A219892.

A219894 Number of directed 2-regular graphs on n nodes without directed 2-cycles.

Original entry on oeis.org

1, 4, 9, 55, 453, 4357, 47598, 569769, 7371560, 102525991, 1525164223

Offset: 5

N. J. A. Sloane, Nov 30 2012

Gunnar Brinkmann, Generating regular directed graphs, Discrete Math., 313 (2012), 1-7.

Cf. A096368, A219889, A219890, A219891, A219892, A219893, A219895.

a(14) and a(15) from Brendan McKay, Mar 12 2019

A219895 Number of directed 3-regular graphs on n nodes without directed 2-cycles.

Original entry on oeis.org

3, 26, 1547, 146487, 16018987, 1985766270, 278601715904

Offset: 7

N. J. A. Sloane, Nov 30 2012

Gunnar Brinkmann, Generating regular directed graphs, Discrete Math., 313 (2012), 1-7.

Cf. A096368, A219889, A219890, A219891, A219892, A219893, A219894.

A255599 Number of (semi-)regular tournaments of order n.

Original entry on oeis.org

1, 1, 1, 1, 1, 5, 3, 85, 15, 13333, 1223, 19434757, 1495297, 276013571133, 18400989629

Offset: 1

Danny Rorabaugh, Feb 27 2015

A tournament of odd order n is regular if the out-degree of each vertex is (n-1)/2. A tournament of even order n is semi-regular if the out-degree of each vertex is n/2-1 or n/2.

B. McKay, Digraphs

Cf. A000568, A096368.

a(1)-a(2) prepended and a(14)-a(15) added by Brendan McKay, Mar 21 2019

cp's OEIS Frontend

A219889 Number of directed 2-regular graphs on n nodes.

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A058338 Number of digraphs with indegree = outdegree at each vertex, or Eulerian digraphs (including disconnected graphs) with n nodes.

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A219890 Number of directed 3-regular graphs on n nodes.

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A219891 Number of directed 4-regular graphs on n nodes.

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A219892 Number of directed 5-regular graphs on n nodes.

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A219893 Number of directed 6-regular graphs on n nodes.

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A219894 Number of directed 2-regular graphs on n nodes without directed 2-cycles.

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A219895 Number of directed 3-regular graphs on n nodes without directed 2-cycles.

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Author

Keywords

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A255599 Number of (semi-)regular tournaments of order n.

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