A303792 Number of connected matchstick graphs on n nodes.

1, 1, 2, 5, 13, 50

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..6.

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

Formula

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

a(n) <= A059103(n).

Example

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).

Crossrefs

Cf. A059103.

Sequence in context: A269068 A098716 A082938 * A059103 A365709 A260709

Adjacent sequences: A303789 A303790 A303791 * A303793 A303794 A303795

Keyword

nonn,hard,more

Author

Eric W. Weisstein, Apr 30 2018

Status

approved