A326223 Number of non-Hamiltonian unlabeled n-vertex digraphs (with loops).

1, 0, 7, 80, 2186, 176398, 43479437

Offset

0,3

Comments

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

Links

Table of n, a(n) for n=0..6.

Gus Wiseman, Non-isomorphic representatives of the a(3) = 80 non-Hamiltonian digraphs.

Formula

a(n) = A000595(n)-A326226(n). - Pontus von Brömssen, Jan 06 2026

Example

Non-isomorphic representatives of the a(2) = 7 digraph edge-sets:
  {}
  {11}
  {12}
  {11,12}
  {11,21}
  {11,22}
  {11,12,22}

Crossrefs

The labeled case is A326220.

The case without loops is A326222.

The undirected case is A246446 (without loops) or A326239 (with loops).

Hamiltonian unlabeled digraphs are A326226.

Unlabeled digraphs not containing a Hamiltonian path are A326224.

Cf. A000595, A002416, A003087, A003216, A283420, A326204, A326218, A326225.

Sequence in context: A085606 A365817 A264691 * A058785 A373441 A171768

Adjacent sequences: A326220 A326221 A326222 * A326224 A326225 A326226

Keyword

nonn,more

Author

Gus Wiseman, Jun 15 2019

Extensions

a(5)-a(6) from Pontus von Brömssen, Jan 06 2026

Status

approved