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A249905 Smallest number of vertices supporting a graph with exactly n Hamiltonian cycles up to direction. 4
2, 1, 5, 4, 5, 6, 5, 6, 6, 7, 6, 7, 5, 8, 6, 7, 6, 7, 6, 7, 7, 8, 7, 7, 6, 8, 7, 7, 7, 8, 7, 8, 7, 7, 7, 8, 6, 8, 7, 8, 7, 8, 8, 8, 8, 7, 8, 8, 7, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 6, 8, 7, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8, 7, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

"Up to direction" means that cycles differing only in starting vertex or direction of traversal are treated as one cycle. a(n) always exists since the wheel graph on n spokes has n cycles.

LINKS

Jeremy Tan, Table of n, a(n) for n = 0..4890

Andreas Björklund, Determinant Sums for Undirected Hamiltonicity, arXiv preprint arXiv:1008.0541 [cs.DS], 2010.

Erich Friedman, Math Magic (September 2012)

EXAMPLE

a(3) = 4 since K_4 has 3 Hamiltonian cycles up to direction.

CROSSREFS

Cf. A244511 (a(n) <= 7), A249906 (records), A305190.

Sequence in context: A266628 A283441 A262219 * A171175 A176053 A259791

Adjacent sequences:  A249902 A249903 A249904 * A249906 A249907 A249908

KEYWORD

nonn,hard

AUTHOR

Jeremy Tan, Nov 08 2014

STATUS

approved

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Last modified April 19 17:46 EDT 2021. Contains 343117 sequences. (Running on oeis4.)