The On-Line Encyclopedia of Integer Sequences (OEIS)

A326208 revision #6

A326208

Number of Hamiltonian labeled simple graphs with n vertices.

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

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OFFSET

0,5

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.

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.

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jun 15 2019

EXTENSIONS

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

STATUS

editing