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 A326208 Number of Hamiltonian labeled simple graphs with n vertices. 10
 0, 1, 0, 1, 10, 218, 10078, 896756, 151676112, 47754337568, 28229412456056, 31665593711174080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS A graph is Hamiltonian if it contains a cycle passing through every vertex exactly once. LINKS Table of n, a(n) for n=0..11. F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version 9766535. Wikipedia, Hamiltonian path Gus Wiseman, The a(5) = 218 simple graphs containing a Hamiltonian cycle. FORMULA A006125(n) = a(n) + A326207(n). MATHEMATICA Table[Length[Select[Subsets[Subsets[Range[n], {2}]], FindHamiltonianCycle[Graph[Range[n], #]]!={}&]], {n, 0, 4}] (* Mathematica 8.0+ *) CROSSREFS The unlabeled version is A003216. The directed version is A326204 (with loops) or A326219 (without loops). Simple graphs not containing a Hamiltonian cycle are A326207. Simple graphs containing a Hamiltonian path are A326206. Cf. A003216, A006125, A057864, A283420. Sequence in context: A305107 A294850 A259189 * A007698 A007699 A024291 Adjacent sequences: A326205 A326206 A326207 * A326209 A326210 A326211 KEYWORD nonn,more AUTHOR Gus Wiseman, Jun 15 2019 EXTENSIONS a(7)-a(11) added using tinygraph by Falk Hüffner, Jun 21 2019 STATUS approved

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Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)