A326216 - OEIS

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A326216

Number of labeled n-vertex digraphs (without loops) not containing a (directed) Hamiltonian path.

1, 1, 1, 16, 772

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

A path is Hamiltonian if it passes through every vertex exactly once.

LINKS

Table of n, a(n) for n=0..4.

Wikipedia, Hamiltonian path

Gus Wiseman, Enumeration of paths and cycles and e-coefficients of incomparability graphs, arXiv:0709.0430 [math.CO], 2007.

FORMULA

A053763(n) = a(n) + A326217(n).

EXAMPLE

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}

MATHEMATICA

Table[Length[Select[Subsets[Select[Tuples[Range[n], 2], UnsameQ@@#&]], FindHamiltonianPath[Graph[Range[n], DirectedEdge@@@#]]=={}&]], {n, 4}] (* Mathematica 10.2+ *)

CROSSREFS

Unlabeled digraphs not containing a Hamiltonian path are A326224.

The undirected case is A326205.

The unlabeled undirected case is A283420.

The case with loops is A326213.

Digraphs (without loops) containing a Hamiltonian path are A326217.

Digraphs (without loops) not containing a Hamiltonian cycle are A326218.

Cf. A000595, A002416, A003024, A003216, A057864, A326206, A326214, A326220, A326221, A326225.

Sequence in context: A134183 A042109 A221061 * A194610 A215171 A224736

Adjacent sequences: A326213 A326214 A326215 * A326217 A326218 A326219

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jun 15 2019

STATUS

approved