A374745 Number of unlabeled (3,6)-tight graphs with n vertices.

1, 1, 1, 4, 26, 375, 11495, 613092, 48185341, 5116473573, 698241355081

Offset: 3

Author

Georg Grasegger, Sep 16 2024

Keywords

• nonn
• more

Comments

A graph G=(V,E) is (3,6)-tight if |E|=3|V|-6 and for every subgraph G'=(V',E') with at least 3 vertices |E'|<=3|V'|-6.

Every minimally rigid graph in 3D (A328419) is (3,6)-tight.

Examples

			The triangle graph and the tetrahdral graph are (3,6)-tight.
		

References

• A. Nixon and E. Ross, Inductive Constructions for Combinatorial Local and Global Rigidity, pages 413-434 of M. Sitharam, A. St. John and J. Sidman, editors, Handbook of Geometric Constraint System Principles, CRC Press, 2019.

Links

• Georg Grasegger, Dataset of (3,6)-tight graphs
• Martin Larsson, Nauty Laman plugin

Crossrefs

Cf. A328419.

Programs

nauty

gensparseg $n -K3 # With Laman plugin; see link.

Extensions

a(12)-a(13) added by Georg Grasegger, Oct 17 2024