A126149 -id:A126149 - cp's OEIS frontend

A246446 Number of nonhamiltonian graphs with n nodes.

0, 2, 3, 8, 26, 108, 661, 6150, 97585, 2700050, 135841840, 12568984762, 2179513027405

Offset: 1

Eric W. Weisstein, Aug 26 2014

Jan Goedgebeur, Barbara Meersman, Carol T. Zamfirescu, Graphs with few Hamiltonian Cycles, arXiv:1812.05650 [math.CO], 2018.
Eric Weisstein's World of Mathematics, Nonhamiltonian Graph
Wikipedia, Hamiltonian path

Cf. A000088 (number of simple graphs on n nodes).
Cf. A003216 (number of Hamiltonian graphs on n nodes).
Cf. A126149 (number of connected nonhamiltonian graphs on n nodes).
The labeled case is A326207.
The directed case is A326223 (with loops) or A326222 (without loops).
Unlabeled simple graphs not containing a Hamiltonian path are A283420.
Cf. A006125, A057864, A326205, A326206.

A000088 = Cases[Import["https://oeis.org/A000088/b000088.txt", "Table"], {, }][[All, 2]];
A003216 = Cases[Import["https://oeis.org/A003216/b003216.txt", "Table"], {, }][[All, 2]];
a[n_] := A000088[[n + 1]] - A003216[[n]];
a /@ Range[13] (* Jean-François Alcover, Jan 02 2020 *)

a(n) = A000088(n) - A003216(n).

a(12) from formula by Falk Hüffner, Aug 13 2017

a(13) added by Jan Goedgebeur, May 07 2019

A374314 Number of graphs of order n with exactly two Hamiltonian cycles.

Original entry on oeis.org

0, 0, 0, 2, 11, 75, 740, 10692, 229068, 7005022, 305866545, 18868736922

Offset: 2

Stefano Spezia, Jul 04 2024

Jan Goedgebeur, Barbara Meersman, and Carol T. Zamfirescu, Graphs with few Hamiltonian Cycles, arXiv:1812.05650 [math.CO], 2018-2019. See Table 6 at p. 27.

Cf. A126149, A307956, A374315, A374316.

A374315 Number of graphs of order n with exactly three Hamiltonian cycles.

Original entry on oeis.org

0, 0, 1, 0, 3, 17, 283, 5069, 132345, 4451059, 209875768, 13364007134

Offset: 2

Stefano Spezia, Jul 04 2024

Jan Goedgebeur, Barbara Meersman, and Carol T. Zamfirescu, Graphs with few Hamiltonian Cycles, arXiv:1812.05650 [math.CO], 2018-2019. See Table 6 at p. 27.

Cf. A126149, A307956, A374314, A374316.

A374316 Number of graphs of order n with at least four Hamiltonian cycles.

Original entry on oeis.org

0, 0, 0, 3, 22, 242, 4691, 154942, 8808453, 867760434, 151839645047, 48280546012319

Offset: 2

Stefano Spezia, Jul 04 2024

Jan Goedgebeur, Barbara Meersman, and Carol T. Zamfirescu, Graphs with few Hamiltonian Cycles, arXiv:1812.05650 [math.CO], 2018-2019. See Table 6 at p. 27.

Cf. A126149, A307956, A374314, A374315.

cp's OEIS Frontend

A246446 Number of nonhamiltonian graphs with n nodes.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A374314 Number of graphs of order n with exactly two Hamiltonian cycles.

Views

Author

Keywords

Links

Crossrefs

A374315 Number of graphs of order n with exactly three Hamiltonian cycles.

Views

Author

Keywords

Links

Crossrefs

A374316 Number of graphs of order n with at least four Hamiltonian cycles.

Views

Author

Keywords

Links

Crossrefs