A326220
Number of non-Hamiltonian labeled n-vertex digraphs (with loops).
Original entry on oeis.org
1, 0, 12, 392, 46432, 20023232, 30595305216
Offset: 0
The a(2) = 12 digraph edge-sets:
{} {11} {11,12} {11,12,22}
{12} {11,21} {11,21,22}
{21} {11,22}
{22} {12,22}
{21,22}
The undirected case is
A326239 (with loops) or
A326207 (without loops).
Digraphs (with loops) containing a Hamiltonian cycle are
A326204.
Digraphs (with loops) not containing a Hamiltonian path are
A326213.
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Table[Length[Select[Subsets[Tuples[Range[n],2]],FindHamiltonianCycle[Graph[Range[n],DirectedEdge@@@#]]=={}&]],{n,4}] (* Mathematica 8.0+. Warning: Using HamiltonianGraphQ instead of FindHamiltonianCycle returns a(4) = 46336 which is incorrect *)
A326223
Number of non-Hamiltonian unlabeled n-vertex digraphs (with loops).
Original entry on oeis.org
1, 0, 7, 80, 2186
Offset: 0
Non-isomorphic representatives of the a(2) = 7 digraph edge-sets:
{}
{11}
{12}
{11,12}
{11,21}
{11,22}
{11,12,22}
The undirected case is
A246446 (without loops) or
A326239 (with loops).
Hamiltonian unlabeled digraphs are
A326226.
Unlabeled digraphs not containing a Hamiltonian path are
A326224.
A326215
Number of Hamiltonian unlabeled n-vertex graphs with loops.
Original entry on oeis.org
Non-isomorphic representatives of the a(3) = 4 edge-sets:
{12,13,23}
{12,13,23,33}
{12,13,22,23,33}
{11,12,13,22,23,33}
A326240
Number of Hamiltonian labeled n-vertex graphs with loops.
Original entry on oeis.org
0, 2, 0, 8, 160, 6976, 644992
Offset: 0
The a(3) = 8 edge-sets:
{12,13,23} {11,12,13,23} {11,12,13,22,23} {11,12,13,22,23,33}
{12,13,22,23} {11,12,13,23,33}
{12,13,23,33} {12,13,22,23,33}
Graphs with loops not containing a Hamiltonian cycle are
A326239.
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Table[Length[Select[Subsets[Select[Tuples[Range[n],2],OrderedQ]],FindHamiltonianCycle[Graph[Range[n],#]]!={}&]],{n,0,5}]
Showing 1-4 of 4 results.
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