OFFSET
0,3
LINKS
Wikipedia, Hamiltonian path
Gus Wiseman, Enumeration of paths and cycles and e-coefficients of incomparability graphs, arXiv:0709.0430 [math.CO], 2007.
EXAMPLE
The a(3) = 48 edge-sets:
{12,23} {12,13,21} {12,13,21,23} {12,13,21,23,31} {12,13,21,23,31,32}
{12,31} {12,13,23} {12,13,21,31} {12,13,21,23,32}
{13,21} {12,13,31} {12,13,21,32} {12,13,21,31,32}
{13,32} {12,13,32} {12,13,23,31} {12,13,23,31,32}
{21,32} {12,21,23} {12,13,23,32} {12,21,23,31,32}
{23,31} {12,21,31} {12,13,31,32} {13,21,23,31,32}
{12,21,32} {12,21,23,31}
{12,23,31} {12,21,23,32}
{12,23,32} {12,21,31,32}
{12,31,32} {12,23,31,32}
{13,21,23} {13,21,23,31}
{13,21,31} {13,21,23,32}
{13,21,32} {13,21,31,32}
{13,23,31} {13,23,31,32}
{13,23,32} {21,23,31,32}
{13,31,32}
{21,23,31}
{21,23,32}
{21,31,32}
{23,31,32}
MATHEMATICA
Table[Length[Select[Subsets[Select[Tuples[Range[n], 2], UnsameQ@@#&]], FindHamiltonianPath[Graph[Range[n], DirectedEdge@@@#]]!={}&]], {n, 4}] (* Mathematica 10.2+ *)
CROSSREFS
The undirected case is A326206.
The unlabeled undirected case is A057864.
The case with loops is A326214.
Unlabeled digraphs with a Hamiltonian path are A326221.
Digraphs (without loops) not containing a Hamiltonian path are A326216.
Digraphs (without loops) containing a Hamiltonian cycle are A326219.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 15 2019
EXTENSIONS
a(5)-a(7) from Bert Dobbelaere, Feb 21 2023
STATUS
approved