A326222 Number of non-Hamiltonian unlabeled n-vertex digraphs (without loops).

1, 0, 2, 12, 157, 5883, 696803, 255954536

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..7.

Gus Wiseman, Non-isomorphic representatives of the a(3) = 12 non-Hamiltonian digraphs.

Formula

a(n) = A000273(n) - A326225(n). - Pontus von Brömssen, Mar 17 2024

Crossrefs

The labeled case is A326218 (without loops) or A326220 (with loops).

The undirected case (without loops) is A246446.

The case with loops is A326223.

Hamiltonian unlabeled digraphs are A326225 (without loops) or A003216 (with loops).

Cf. A000273, A000595, A002416, A003087, A053763, A326216, A326217, A326224, A326226.

Sequence in context: A075631 A127182 A330552 * A208577 A012646 A177778

Adjacent sequences: A326219 A326220 A326221 * A326223 A326224 A326225

Keyword

nonn,hard,more

Author

Gus Wiseman, Jun 15 2019

Extensions

a(5)-a(7) (using A000273 and A326225) from Pontus von Brömssen, Mar 17 2024

Status

approved