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 A326239 Number of non-Hamiltonian labeled n-vertex graphs with loops. 4
 1, 0, 8, 56, 864, 25792 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A graph is Hamiltonian if it contains a cycle passing through every vertex exactly once. LINKS Wikipedia, Hamiltonian path 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. Cf. A000088, A003216, A006125, A057864, A283420. Sequence in context: A208944 A209072 A133671 * A154411 A105850 A009089 Adjacent sequences: A326236 A326237 A326238 * A326240 A326241 A326242 KEYWORD nonn,more AUTHOR Gus Wiseman, Jun 16 2019 STATUS approved

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Last modified March 28 17:47 EDT 2023. Contains 361596 sequences. (Running on oeis4.)