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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
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.
Sequence in context: A333981 A030243 A222789 * A088077 A358326 A162079
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