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A326207 Number of non-Hamiltonian labeled simple graphs with n vertices.

%I A326207 #10 Jun 21 2019 07:57:57
%S A326207 1,0,2,7,54,806,22690,1200396,116759344,20965139168,6954959632776,
%T A326207 4363203307789888
%N A326207 Number of non-Hamiltonian labeled simple graphs with n vertices.
%C A326207 A graph is Hamiltonian if it contains a cycle passing through every vertex exactly once.
%H A326207 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hamiltonian_path">Hamiltonian path</a>
%F A326207 A006125(n) = a(n) + A326208(n).
%e A326207 The a(3) = 7 edge sets:
%e A326207   {}
%e A326207   {12}
%e A326207   {13}
%e A326207   {23}
%e A326207   {12,13}
%e A326207   {12,23}
%e A326207   {13,23}
%t A326207 Table[Length[Select[Subsets[Subsets[Range[n],{2}]],FindHamiltonianCycle[Graph[Range[n],#]]=={}&]],{n,0,4}] (* Mathematica 8.0+ *)
%Y A326207 The unlabeled version is A246446.
%Y A326207 The directed version is A326220 (with loops) or A326216 (without loops).
%Y A326207 Simple graphs with a Hamiltonian cycle are A326208.
%Y A326207 Simple graphs without a Hamiltonian path are A326205.
%Y A326207 Cf. A003216, A006125, A057864, A283420.
%K A326207 nonn,more
%O A326207 0,3
%A A326207 _Gus Wiseman_, Jun 15 2019
%E A326207 a(7)-a(11) from formula by _Falk Hüffner_, Jun 21 2019