A326208 Number of Hamiltonian labeled simple graphs with n vertices.

0, 1, 0, 1, 10, 218, 10078, 896756, 151676112, 47754337568, 28229412456056, 31665593711174080

Offset

0,5

Comments

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

Links

Table of n, a(n) for n=0..11.

F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version 9766535.

Wikipedia, Hamiltonian path

Gus Wiseman, The a(5) = 218 simple graphs containing a Hamiltonian cycle.

Formula

A006125(n) = a(n) + A326207(n).

Mathematica

Table[Length[Select[Subsets[Subsets[Range[n], {2}]], FindHamiltonianCycle[Graph[Range[n], #]]!={}&]], {n, 0, 4}] (* Mathematica 8.0+ *)

Crossrefs

The unlabeled version is A003216.

The directed version is A326204 (with loops) or A326219 (without loops).

Simple graphs not containing a Hamiltonian cycle are A326207.

Simple graphs containing a Hamiltonian path are A326206.

Cf. A003216, A006125, A057864, A283420.

Sequence in context: A305107 A294850 A259189 * A007698 A007699 A024291

Adjacent sequences: A326205 A326206 A326207 * A326209 A326210 A326211

Keyword

nonn,more

Author

Gus Wiseman, Jun 15 2019

Extensions

a(7)-a(11) added using tinygraph by Falk Hüffner, Jun 21 2019

Status

approved