A326225 Number of Hamiltonian unlabeled n-vertex digraphs (without loops).

0, 1, 1, 4, 61, 3725, 844141, 626078904

Offset: 0

Author

Gus Wiseman, Jun 15 2019

Keywords

• nonn
• hard
• more

Comments

A digraph is Hamiltonian if it contains a directed cycle passing through every vertex exactly once.

Examples

			Non-isomorphic representatives of the a(3) = 4 digraph edge-sets:
  {12,23,31}
  {12,13,21,32}
  {12,13,21,23,31}
  {12,13,21,23,31,32}
		

Links

• Sean A. Irvine, Non-isomorphic representatives of the a(5) = 3725 non-Hamiltonian digraphs (without loops)
• Gus Wiseman, Non-isomorphic representatives of the a(4) = 61 non-Hamiltonian digraphs (without loops)

Crossrefs

The labeled case is A326219.

The case with loops is A326226.

The undirected case is A003216.

Non-Hamiltonian unlabeled digraphs (without loops) are A326222.

Cf. A000595, A002416, A003087, A003216, A053763, A246446, A326204, A326218, A326223.

Extensions

a(5)-a(7) from Sean A. Irvine, Jun 16 2019