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 A326206 Number of n-vertex labeled simple graphs containing a Hamiltonian path. 10
 0, 0, 1, 4, 34, 633, 23368, 1699012, 237934760, 64558137140, 34126032806936, 35513501049012952 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A path is Hamiltonian if it passes through every vertex exactly once. LINKS F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version 9766535. Wikipedia, Hamiltonian path FORMULA A006125(n) = a(n) + A326205(n). MATHEMATICA Table[Length[Select[Subsets[Subsets[Range[n], {2}]], FindHamiltonianPath[Graph[Range[n], #]]!={}&]], {n, 0, 4}] (* Mathematica 10.2+ *) CROSSREFS The unlabeled case is A057864. The directed case is A326214 (with loops) or A326217 (without loops). Simple graphs without a Hamiltonian path are A326205. Simple graphs with a Hamiltonian cycle are A326208. Cf. A003216, A006125, A057864, A283420. Sequence in context: A333981 A030243 A222789 * A088077 A162079 A353041 Adjacent sequences:  A326203 A326204 A326205 * A326207 A326208 A326209 KEYWORD nonn,more AUTHOR Gus Wiseman, Jun 14 2019 EXTENSIONS a(7)-a(11) added using tinygraph by Falk Hüffner, Jun 21 2019 STATUS approved

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Last modified May 21 06:36 EDT 2022. Contains 353889 sequences. (Running on oeis4.)