A386962 Number of equivalence classes of connected 3-regular graphs on 2n unlabeled nodes up to local complementation.

0, 1, 2, 4, 15, 60

Offset: 1

Author

Tristan Cam, Aug 11 2025

Keywords

• nonn
• more
• new

Comments

Number of equivalences classes of 3-regular graphs on 2n nodes up to a sequence of local complementation or isomorphism, also called orbits for the local equivalence relation.

a(n) is necessarily less than:

A005638(n) (number of non-isomorphic, not necessarily connected 3-regular graphs);

A002851(n) (number of non-isomophic connected 3-regular graphs);

A090899(n) (number of local equivalence classes of connected graphs); and

A156800(n) (number of equivalence classes for connected graphs up to pivots and isomorphism).

This is relevant in the study of optimal quantum circuit synthesis for graph state preparation.

Examples

			There are only two 3-regular graphs with 6 nodes and they are not equivalent up to a sequence of local complementation, thus a(3) = 2.
		

Links

• Niels Bohr Institute Center for Hybrid Quantum Networks, graph_table (github)
• Tristan Cam, Cyril Gavoille, Yvan Le Borgne, and Simon Martiel, Universal Graph Theory Operations for Graph State Preparation

Crossrefs

Cf. A002851, A005638, A090899, A156800.