A303792 Number of connected matchstick graphs on n nodes.

1, 1, 2, 5, 13, 50

Offset: 1

Author

Eric W. Weisstein, Apr 30 2018

Keywords

• nonn
• hard
• more

Comments

a(7) >= 211. - Eric W. Weisstein, Jan 02 2022

Examples

			a(6) is one less than A059103(6) because the 3-prism graph Y_3 cannot be drawn in an embedding that is both planar and unit-distance.
There are 11 connected graphs on 7 nodes that are unit-distance but non-matchstick (including Y_3+e and the Moser spindle).
		

Links

• Jaskaran Singh Grover, Changliu Liu and Katia Sycara, Deadlock Analysis and Resolution for Multi-Robot Systems, (2020).
• Eric Weisstein's World of Mathematics, Connected Graph
• Eric Weisstein's World of Mathematics, Matchstick Graph

Crossrefs

Cf. A059103.

Formula

a(6) = A059103(6) - 1.

a(n) <= A059103(n).