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A326204
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Number of Hamiltonian labeled n-vertex digraphs (with loops).
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12
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OFFSET
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0,2
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COMMENTS
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A digraph is Hamiltonian if it contains a directed cycle passing through every vertex exactly once.
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LINKS
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EXAMPLE
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The a(2) = 4 digraph edge-sets:
{12,21}
{11,12,21}
{12,21,22}
{11,12,21,22}
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MATHEMATICA
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Table[Length[Select[Subsets[Tuples[Range[n], 2]], FindHamiltonianCycle[Graph[Range[n], DirectedEdge@@@#]]!={}&]], {n, 0, 4}] (* Mathematica 8.0+. Warning: Using HamiltonianGraphQ instead of FindHamiltonianCycle returns a(4) = 19200 which is incorrect *)
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CROSSREFS
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The undirected case (without loops) is A326208.
Non-Hamiltonian digraphs are A326220.
Digraphs containing a Hamiltonian path are A326214.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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