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A326207 Number of non-Hamiltonian labeled simple graphs with n vertices. 5
1, 0, 2, 7, 54, 806, 22690, 1200396, 116759344, 20965139168, 6954959632776, 4363203307789888 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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.

Wikipedia, Hamiltonian path

FORMULA

A006125(n) = a(n) + A326208(n).

EXAMPLE

The a(3) = 7 edge sets:

  {}

  {12}

  {13}

  {23}

  {12,13}

  {12,23}

  {13,23}

MATHEMATICA

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

CROSSREFS

The unlabeled version is A246446.

The directed version is A326220 (with loops) or A326216 (without loops).

Simple graphs with a Hamiltonian cycle are A326208.

Simple graphs without a Hamiltonian path are A326205.

Cf. A003216, A006125, A057864, A283420.

Sequence in context: A024027 A079410 A283335 * A280221 A227381 A182055

Adjacent sequences:  A326204 A326205 A326206 * A326208 A326209 A326210

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jun 15 2019

EXTENSIONS

a(7)-a(11) from formula by Falk Hüffner, Jun 21 2019

STATUS

approved

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Last modified May 14 10:15 EDT 2021. Contains 343880 sequences. (Running on oeis4.)