A306827 -id:A306827 - 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)

A306892 Isomorphism classes of connected 2-regular digraphs on n nodes, allowing multiarcs and loops.

Original entry on oeis.org

1, 1, 2, 5, 14, 50, 265, 1601, 11984, 101884

Offset: 0

R. J. Mathar, Mar 15 2019

The graphs are directed, connected and have indegree=outdegree=2 at each node. Multiarcs (connecting two nodes with the same sense of heading) and loops (edges connecting a node to itself) are permitted.

The sequence of the same family of graphs which are not necessarily connected is A006372 (the Euler transform of this sequence).

			On n=1 node, the graph is the node with two edges looping back to the node.
On n=2 nodes, the graph is either having two pairs of edges (4 edges in total) linking one node to the other, or a loop at each node and two edges (different senses) from one node to the other.

R. J. Mathar, OEIS A306892
R. J. Mathar, 2-regular digraphs of the Lovelock Lagrangian, arXiv:1903.12477 [math.GM] (2019).

Cf. A306827 (no loops).

a(8) added by R. J. Mathar, Apr 08 2019

a(9) added by R. J. Mathar, Apr 15 2019

A307180 Isomorphism classes of 2-in 2-out regular digraphs, allowing parallel edges but not loops.

Original entry on oeis.org

1, 0, 1, 2, 6, 15, 68, 310, 2096, 16554, 152497, 1574652, 17947667, 223013311

Offset: 0

R. J. Mathar, Mar 28 2019

Richard J. Mathar, 2-regular Digraphs of the Lovelock Lagrangian, arXiv:1903.12477 [math.GM], 2019.

Cf. A306827 (connected, inverse Eul. Trans.)

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

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A306892 Isomorphism classes of connected 2-regular digraphs on n nodes, allowing multiarcs and loops.

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A307180 Isomorphism classes of 2-in 2-out regular digraphs, allowing parallel edges but not loops.

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