A084656 - OEIS

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

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OFFSET

1,6

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).

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

Table of n, a(n) for n=1..18.

Gordon Royle, Combinatorial Data.

EXAMPLE

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.

CROSSREFS

Cf. A084657, A084658, A057848.

Sequence in context: A032020 A261962 A301500 * A073749 A299590 A250396

Adjacent sequences: A084653 A084654 A084655 * A084657 A084658 A084659

KEYWORD

nonn,more

AUTHOR

Gordon F. Royle, Jun 02 2003

EXTENSIONS

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

STATUS

approved