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A326216
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Number of labeled n-vertex digraphs (without loops) not containing a (directed) Hamiltonian path.
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6
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OFFSET
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0,4
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COMMENTS
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A path is Hamiltonian if it passes through every vertex exactly once.
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LINKS
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FORMULA
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EXAMPLE
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The a(3) = 16 edge-sets:
{} {12} {12,13}
{13} {12,21}
{21} {12,32}
{23} {13,23}
{31} {13,31}
{32} {21,23}
{21,31}
{23,32}
{31,32}
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MATHEMATICA
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Table[Length[Select[Subsets[Select[Tuples[Range[n], 2], UnsameQ@@#&]], FindHamiltonianPath[Graph[Range[n], DirectedEdge@@@#]]=={}&]], {n, 4}] (* Mathematica 10.2+ *)
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CROSSREFS
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Unlabeled digraphs not containing a Hamiltonian path are A326224.
The unlabeled undirected case is A283420.
Digraphs (without loops) containing a Hamiltonian path are A326217.
Digraphs (without loops) not containing a Hamiltonian cycle are A326218.
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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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