A326240 Number of Hamiltonian labeled n-vertex graphs with loops.

0, 2, 0, 8, 160, 6976, 644992

Offset: 0

Author

Gus Wiseman, Jun 17 2019

Keywords

• nonn
• more

Comments

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

Examples

			The a(3) = 8 edge-sets:
  {12,13,23}  {11,12,13,23}  {11,12,13,22,23}  {11,12,13,22,23,33}
              {12,13,22,23}  {11,12,13,23,33}
              {12,13,23,33}  {12,13,22,23,33}
		

Crossrefs

The unlabeled case is A326215.

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

The case without loops A326208.

Graphs with loops not containing a Hamiltonian cycle are A326239.

Cf. A000088, A003216, A006125, A057864, A283420.

Programs

Mathematica

Table[Length[Select[Subsets[Select[Tuples[Range[n],2],OrderedQ]],FindHamiltonianCycle[Graph[Range[n],#]]!={}&]],{n,0,5}]

Formula

a(n) = A326208(n) * 2^n.