A326208 Number of Hamiltonian labeled simple graphs with n vertices.

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

Offset: 0

Author

Gus Wiseman, Jun 15 2019

Keywords

• nonn
• more

Comments

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

Links

• 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.

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.

Programs

Mathematica

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

Formula

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

Extensions

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