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 A326207 Number of non-Hamiltonian labeled simple graphs with n vertices. 5
 1, 0, 2, 7, 54, 806, 22690, 1200396, 116759344, 20965139168, 6954959632776, 4363203307789888 (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 FORMULA A006125(n) = a(n) + A326208(n). EXAMPLE The a(3) = 7 edge sets:   {}   {12}   {13}   {23}   {12,13}   {12,23}   {13,23} MATHEMATICA Table[Length[Select[Subsets[Subsets[Range[n], {2}]], FindHamiltonianCycle[Graph[Range[n], #]]=={}&]], {n, 0, 4}] (* Mathematica 8.0+ *) CROSSREFS The unlabeled version is A246446. The directed version is A326220 (with loops) or A326216 (without loops). Simple graphs with a Hamiltonian cycle are A326208. Simple graphs without a Hamiltonian path are A326205. Cf. A003216, A006125, A057864, A283420. Sequence in context: A024027 A079410 A283335 * A280221 A227381 A182055 Adjacent sequences:  A326204 A326205 A326206 * A326208 A326209 A326210 KEYWORD nonn,more AUTHOR Gus Wiseman, Jun 15 2019 EXTENSIONS a(7)-a(11) from formula by Falk Hüffner, Jun 21 2019 STATUS approved

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Last modified May 14 10:15 EDT 2021. Contains 343880 sequences. (Running on oeis4.)