A249905 Smallest number of vertices supporting a graph with exactly n Hamiltonian cycles up to direction.

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

Offset: 0

Author

Jeremy Tan, Nov 08 2014

Keywords

• nonn
• hard

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.

Examples

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

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)

Crossrefs

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