cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A249906 a(n) is the index of the first occurrence of n in A249905, or -1 if n does not occur.

Original entry on oeis.org

1, 0, -1, 3, 2, 5, 9, 13, 89, 485, 4891
Offset: 1

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Author

Jeremy Tan, Nov 08 2014

Keywords

Comments

a(n) is the smallest number of Hamiltonian cycles up to direction which requires at least an n-vertex graph to realize.

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Extensions

a(10)-a(11) using data from Johan de Ruiter added by Jeremy Tan, Nov 02 2018

A244511 Possible numbers of Hamiltonian cycles up to direction in 7-vertex graphs.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 26, 27, 28, 30, 32, 33, 34, 36, 38, 40, 45, 48, 52, 60, 62, 70, 72, 76, 80, 90, 108, 120, 144, 168, 240, 360
Offset: 1

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Author

Jeremy Tan, Nov 11 2014

Keywords

Examples

			The empty graph on 7 vertices has no Hamiltonian cycles, so a(1) = 0. The cycle graph C_7 has exactly one so a(2) = 1.

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Crossrefs

Cf. A249905 (for the definition of "up to direction"), A249906, A253648 (numbers of Hamiltonian cycles that are not possible in 8-vertex graphs), A305190.

A321593 Smallest number of vertices supporting a graph with exactly n Hamiltonian paths.

Original entry on oeis.org

4, 1, 4, 3, 4, 5, 4, 5, 6, 7, 5, 6, 4, 7, 5, 7, 6, 6, 5, 7, 6, 7, 6, 7, 5, 7, 6, 8, 6, 7, 6, 7, 6, 7, 6, 7, 5, 7, 6, 7, 6, 8, 7, 7, 7, 6, 7, 7, 6, 8, 7, 7, 7, 7, 7, 7, 7, 8, 7, 8, 5, 7, 6, 7, 8, 7, 7, 7, 7, 7, 6, 7, 6, 8, 7, 7, 6, 8, 7, 7, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 6, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 7
Offset: 0

Views

Author

Jeremy Tan, Nov 14 2018

Keywords

Comments

The reverse of a path is counted as the same path. a(n) is well-defined as the cycle graph C_n has n paths.
a(n) >= A249905(n) - 1, since the number of Hamiltonian paths in G is the same as the number of Hamiltonian cycles in H, where H is G with a new vertex connected to all vertices in G.

Examples

			a(12) = 4 since K_4 has 12 Hamiltonian paths, and no graph on less than 4 vertices has 12 Hamiltonian paths.

Links

Crossrefs

The corresponding sequence for Hamiltonian cycles is A249905.
Showing 1-3 of 3 results.

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