

A059103


Number of simple, connected, unitdistance graphs on n points realizable in the plane with straight edges all of the same length; lines are permitted to cross.


4




OFFSET

1,3


COMMENTS

This counting problem is related to finding the chromatic number of the plane, X(R^2).


REFERENCES

K. B. Chilakamarri and C. R. Mahoney, Maximal and minimal forbidden unitdistance graphs in the plane, Bulletin of the ICA, 13 (1995), 3543.


LINKS

Table of n, a(n) for n=1..9.
Aidan Globus and Hans Parshall, Small unitdistance graphs in the plane, [math.CO] arXiv:1905.07829, 2019.
Matthew McAndrews, Simple Connected Units Distance Graphs Through 6 Vertices
Eric Weisstein's World of Mathematics, Connected Graph
Eric Weisstein's World of Mathematics, UnitDistance Graph


EXAMPLE

a(4)=5 because the complete graph on 4 points cannot be realized in the plane with all edges of equal length. All the other connected graphs with 4 points can be realized.


CROSSREFS

Cf. A303792 (number of connected matchstick graphs).
Cf. A308349 (number of minimal unitdistance forbidden graphs).
Sequence in context: A098716 A082938 A303792 * A260709 A112836 A105905
Adjacent sequences: A059100 A059101 A059102 * A059104 A059105 A059106


KEYWORD

hard,more,nonn


AUTHOR

David S. Newman, Feb 13 2001


EXTENSIONS

a(6) has been updated to reflect the fact that it has recently been proved to be 51 rather than 50.  Matthew McAndrews, Feb 21 2016
a(7) from Hans Parshall, May 03 2018
a(8)a(9) from Hans Parshall, May 21 2019


STATUS

approved



