A249905 - OEIS

%I #16 Aug 13 2020 14:02:28

%S 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,

%T 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,

%U 8,8,7,8,7,8,8,8,7,8,8,8,7,8,8,8,8,8,8,8,8,9

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

%C "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.

%H Jeremy Tan, <a href="/A249905/b249905.txt">Table of n, a(n) for n = 0..4890</a>

%H Andreas Björklund, <a href="http://arxiv.org/abs/1008.0541">Determinant Sums for Undirected Hamiltonicity</a>, arXiv preprint arXiv:1008.0541 [cs.DS], 2010.

%H Erich Friedman, <a href="https://erich-friedman.github.io/mathmagic/0912.html">Math Magic</a> (September 2012)

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

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

%K nonn,hard

%O 0,1

%A _Jeremy Tan_, Nov 08 2014