A326224 Number of unlabeled n-vertex digraphs (with loops) not containing a Hamiltonian path.

1, 2, 3, 30, 649

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) = 30 digraphs not containing a Hamiltonian path.

Crossrefs

The labeled case is A326213.

The undirected case is A283420 (without loops).

Unlabeled digraphs containing a Hamiltonian path are A326221.

Unlabeled digraphs not containing a Hamiltonian cycle are A326223.

Cf. A000595, A002416, A003087, A003216, A057864.

Formula

A000595(n) = a(n) + A326221(n).