A326204 Number of Hamiltonian labeled n-vertex digraphs (with loops).

0, 2, 4, 120, 19104

Offset: 0

Author

Gus Wiseman, Jun 14 2019

Keywords

• nonn
• more

Comments

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

Examples

			The a(2) = 4 digraph edge-sets:
  {12,21}
  {11,12,21}
  {12,21,22}
  {11,12,21,22}
		

Links

• Wikipedia, Hamiltonian path

Crossrefs

The unlabeled case is A326226.

The case without loops is A326219.

The undirected case (without loops) is A326208.

Non-Hamiltonian digraphs are A326220.

Digraphs containing a Hamiltonian path are A326214.

Cf. A000595, A002416, A003024, A003216, A057864.

Programs

Mathematica

Table[Length[Select[Subsets[Tuples[Range[n],2]],FindHamiltonianCycle[Graph[Range[n],DirectedEdge@@@#]]!={}&]],{n,0,4}] (* Mathematica 8.0+. Warning: Using HamiltonianGraphQ instead of FindHamiltonianCycle returns a(4) = 19200 which is incorrect *)