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

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

Offset

0,2

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..6.

Formula

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

Example

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}

Mathematica

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

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.

Sequence in context: A328920 A033836 A185159 * A009099 A193247 A373697

Adjacent sequences: A326237 A326238 A326239 * A326241 A326242 A326243

Keyword

nonn,more

Author

Gus Wiseman, Jun 17 2019

Status

approved