A326208 - OEIS

%I #9 Jun 21 2019 07:57:40

%S 0,1,0,1,10,218,10078,896756,151676112,47754337568,28229412456056,

%T 31665593711174080

%N Number of Hamiltonian labeled simple graphs with n vertices.

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

%H F. Hüffner, <a href="https://github.com/falk-hueffner/tinygraph">tinygraph</a>, software for generating integer sequences based on graph properties, version 9766535.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hamiltonian_path">Hamiltonian path</a>

%H Gus Wiseman, <a href="/A326208/a326208.png">The a(5) = 218 simple graphs containing a Hamiltonian cycle.</a>

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

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

%Y The unlabeled version is A003216.

%Y The directed version is A326204 (with loops) or A326219 (without loops).

%Y Simple graphs not containing a Hamiltonian cycle are A326207.

%Y Simple graphs containing a Hamiltonian path are A326206.

%Y Cf. A003216, A006125, A057864, A283420.

%K nonn,more

%O 0,5

%A _Gus Wiseman_, Jun 15 2019

%E a(7)-a(11) added using tinygraph by _Falk Hüffner_, Jun 21 2019