A084656 Number of unlabeled connected claw-free cubic graphs on 2n vertices.

0, 1, 1, 1, 1, 3, 3, 5, 11, 15, 27, 54, 94, 181, 369, 731, 1502, 3187

Offset: 1

Author

Gordon F. Royle, Jun 02 2003

Keywords

• nonn
• more

Comments

A cubic graph is claw-free (contains no induced K_{1,3}) if and only if every vertex lies in a triangle. All graphs counted are simple (no loops or multiple edges).

Examples

			K_4 is claw-free and so a(2) = 1, while the triangular prism is the only claw-free cubic graph on 6 vertices, so a(3) = 1.
		

References

• A. Itzhakov and M. Codish, Breaking Symmetries with High Dimensional Graph Invariants and their Combination, Proceedings of the 20th International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research (2023).

Links

• Gordon Royle, Combinatorial Data.

Crossrefs

Cf. A084657, A084658, A057848.

Extensions

a(16)-a(18) from Michael Codish, Mar 05 2023