login
A326219
Number of labeled n-vertex Hamiltonian digraphs (without loops).
7
0, 1, 1, 15, 1194
OFFSET
0,4
COMMENTS
A digraph is Hamiltonian if it contains a directed cycle passing through every vertex exactly once.
FORMULA
A053763(n) = a(n) + A326218(n).
EXAMPLE
The a(3) = 15 edge-sets:
{12,23,31} {12,13,21,32} {12,13,21,23,31} {12,13,21,23,31,32}
{13,21,32} {12,13,23,31} {12,13,21,23,32}
{12,21,23,31} {12,13,21,31,32}
{12,23,31,32} {12,13,23,31,32}
{13,21,23,32} {12,21,23,31,32}
{13,21,31,32} {13,21,23,31,32}
MATHEMATICA
Table[Length[Select[Subsets[Select[Tuples[Range[n], 2], UnsameQ@@#&]], FindHamiltonianCycle[Graph[Range[n], DirectedEdge@@@#]]!={}&]], {n, 0, 4}] (* Mathematica 8.0+. Warning: Using HamiltonianGraphQ instead of FindHamiltonianCycle returns a(4) = 1200 which is incorrect *)
CROSSREFS
The unlabeled case is A326225.
The undirected case is A326208 (without loops) or A326240 (with loops).
The case with loops is A326204.
Digraphs (without loops) not containing a Hamiltonian cycle are A326218.
Digraphs (without loops) containing a Hamiltonian path are A326217.
Sequence in context: A230669 A027492 A001728 * A211901 A059383 A206394
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 15 2019
STATUS
approved