

A326220


Number of nonHamiltonian labeled nvertex digraphs (with loops).


8




OFFSET

0,3


COMMENTS

A digraph is Hamiltonian if it contains a directed cycle passing through every vertex exactly once.


LINKS

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


EXAMPLE

The a(2) = 12 digraph edgesets:
{} {11} {11,12} {11,12,22}
{12} {11,21} {11,21,22}
{21} {11,22}
{22} {12,22}
{21,22}


MATHEMATICA

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 *)


CROSSREFS

The unlabeled case is A326223.
The undirected case is A326239 (with loops) or A326207 (without loops).
The case without loops is A326218.
Digraphs (with loops) containing a Hamiltonian cycle are A326204.
Digraphs (with loops) not containing a Hamiltonian path are A326213.
Cf. A000595, A002416, A003024, A003216, A246446, A326208, A326219, A326222, A326224.
Sequence in context: A326214 A187513 A138914 * A308129 A286038 A276482
Adjacent sequences: A326217 A326218 A326219 * A326221 A326222 A326223


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Jun 15 2019


STATUS

approved



