This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A326226 Number of unlabeled n-vertex Hamiltonian digraphs (with loops). 10
 0, 2, 3, 24, 858 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A digraph is Hamiltonian if it contains a directed cycle passing through every vertex exactly once. LINKS Wikipedia, Hamiltonian path EXAMPLE Non-isomorphic representatives of the a(2) = 3 digraph edge-sets:   {12,21}   {11,12,21}   {11,12,21,22} MATHEMATICA dinorm[m_]:=If[m=={}, {}, If[Union@@m!=Range[Max@@Flatten[m]], dinorm[m/. Apply[Rule, Table[{(Union@@m)[[i]], i}, {i, Length[Union@@m]}], {1}]], First[Sort[dinorm[m, 1]]]]]; dinorm[m_, aft_]:=If[Length[Union@@m]<=aft, {m}, With[{mx=Table[Count[m, i, {2}], {i, Select[Union@@m, #1>=aft&]}]}, Union@@(dinorm[#1, aft+1]&)/@Union[Table[Map[Sort, m/. {par+aft-1->aft, aft->par+aft-1}, {0}], {par, First/@Position[mx, Max[mx]]}]]]]; Table[Length[Select[Union[dinorm/@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) = 867 which is incorrect *) CROSSREFS The labeled case is A326204. The case without loops is A326225. The undirected case is A003216 (without loops) or A326215 (with loops). Unlabeled non-Hamiltonian digraphs are A326223. Unlabeled digraphs with a Hamiltonian path are A326221. Cf. A000595, A002416, A003087, A057864, A246446, A326208. Sequence in context: A013312 A013318 A193338 * A291262 A307922 A048674 Adjacent sequences:  A326223 A326224 A326225 * A326227 A326228 A326229 KEYWORD nonn,hard,more AUTHOR Gus Wiseman, Jun 14 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 21 04:22 EST 2019. Contains 329350 sequences. (Running on oeis4.)