A326221 Number of unlabeled n-vertex digraphs (with loops) containing a Hamiltonian path.

0, 0, 7, 74, 2395

Offset: 0

Author

Gus Wiseman, Jun 16 2019

Keywords

• nonn
• more

Comments

A directed path is Hamiltonian if it passes through every vertex exactly once.

Links

• Wikipedia, Hamiltonian path
• Gus Wiseman, Enumeration of paths and cycles and e-coefficients of incomparability graphs, arXiv:0709.0430 [math.CO], 2007.
• Gus Wiseman, Non-isomorphic representatives of the a(3) = 74 digraphs containing a Hamiltonian path.

Crossrefs

The labeled case is A326214.

The undirected case is A057864 (without loops).

Unlabeled digraphs not containing a Hamiltonian path are A326224.

Unlabeled digraphs containing a Hamiltonian cycle are A326226.

Cf. A000595, A002416, A003087, A003216, A283420.

Formula

A000595(n) = a(n) + A326224(n).