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A326239
Number of non-Hamiltonian labeled n-vertex graphs with loops.
4
1, 0, 8, 56, 864, 25792
OFFSET
0,3
COMMENTS
A graph is Hamiltonian if it contains a cycle passing through every vertex exactly once.
EXAMPLE
The a(3) = 56 edge-sets:
{} {11} {11,12} {11,12,13}
{12} {11,13} {11,12,22}
{13} {11,22} {11,12,23}
{22} {11,23} {11,12,33}
{23} {11,33} {11,13,22}
{33} {12,13} {11,13,23}
{12,22} {11,13,33}
{12,23} {11,22,23}
{12,33} {11,22,33}
{13,22} {11,23,33}
{13,23} {12,13,22}
{13,33} {12,13,33}
{22,23} {12,22,23}
{22,33} {12,22,33}
{23,33} {12,23,33}
{13,22,23}
{13,22,33}
{13,23,33}
{22,23,33}
MATHEMATICA
Table[Length[Select[Subsets[Select[Tuples[Range[n], 2], OrderedQ]], FindHamiltonianCycle[Graph[Range[n], #]]=={}&]], {n, 0, 4}]
CROSSREFS
The directed case is A326204 (with loops) or A326218 (without loops).
Simple graphs containing a Hamiltonian cycle are A326240.
Simple graphs not containing a Hamiltonian path are A326205.
Sequence in context: A208944 A209072 A133671 * A154411 A105850 A009089
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 16 2019
STATUS
approved