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A326239 Number of non-Hamiltonian labeled n-vertex graphs with loops.

%I A326239 #7 Sep 03 2019 09:53:13
%S A326239 1,0,8,56,864,25792
%N A326239 Number of non-Hamiltonian labeled n-vertex graphs with loops.
%C A326239 A graph is Hamiltonian if it contains a cycle passing through every vertex exactly once.
%H A326239 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hamiltonian_path">Hamiltonian path</a>
%e A326239 The a(3) = 56 edge-sets:
%e A326239   {}  {11}  {11,12}  {11,12,13}
%e A326239       {12}  {11,13}  {11,12,22}
%e A326239       {13}  {11,22}  {11,12,23}
%e A326239       {22}  {11,23}  {11,12,33}
%e A326239       {23}  {11,33}  {11,13,22}
%e A326239       {33}  {12,13}  {11,13,23}
%e A326239             {12,22}  {11,13,33}
%e A326239             {12,23}  {11,22,23}
%e A326239             {12,33}  {11,22,33}
%e A326239             {13,22}  {11,23,33}
%e A326239             {13,23}  {12,13,22}
%e A326239             {13,33}  {12,13,33}
%e A326239             {22,23}  {12,22,23}
%e A326239             {22,33}  {12,22,33}
%e A326239             {23,33}  {12,23,33}
%e A326239                      {13,22,23}
%e A326239                      {13,22,33}
%e A326239                      {13,23,33}
%e A326239                      {22,23,33}
%t A326239 Table[Length[Select[Subsets[Select[Tuples[Range[n],2],OrderedQ]],FindHamiltonianCycle[Graph[Range[n],#]]=={}&]],{n,0,4}]
%Y A326239 The directed case is A326204 (with loops) or A326218 (without loops).
%Y A326239 Simple graphs containing a Hamiltonian cycle are A326240.
%Y A326239 Simple graphs not containing a Hamiltonian path are A326205.
%Y A326239 Cf. A000088, A003216, A006125, A057864, A283420.
%K A326239 nonn,more
%O A326239 0,3
%A A326239 _Gus Wiseman_, Jun 16 2019