A283420 Number of simple (not necessarily connected) untraceable graphs on n nodes.

0, 1, 2, 6, 16, 65, 310, 2316, 26241, 522596, 18766354

Offset

1,3

Links

Table of n, a(n) for n=1..11.

Eric Weisstein's World of Mathematics, Untraceable Graph

Wikipedia, Hamiltonian path

Gus Wiseman, Enumeration of paths and cycles and e-coefficients of incomparability graphs, arXiv:0709.0430 [math.CO], 2007.

Gus Wiseman, The a(5) = 16 unlabeled simple graphs not containing a Hamiltonian path.

Formula

a(n) = A000088(n) - A057864(n).

Crossrefs

Cf. A000088 (number of simple graphs on n vertices).

Cf. A057864 (number of simple traceable graphs on n vertices).

Cf. A283421 (number of simple connected untraceable graphs on n vertices).

The labeled case is A326205.

The directed case is A326224 (with loops).

Unlabeled simple graphs not containing a Hamiltonian cycle are A246446.

Cf. A003216, A326206, A326217, A326221.

Sequence in context: A173994 A363587 A150032 * A121749 A009386 A009605

Adjacent sequences: A283417 A283418 A283419 * A283421 A283422 A283423

Keyword

nonn,more

Author

Eric W. Weisstein, May 14 2017

Status

approved