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A059103 Number of simple, connected, unit-distance graphs on n points realizable in the plane with straight edges all of the same length; lines are permitted to cross. 4

%I

%S 1,1,2,5,13,51,222,1313,9639

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

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

%D K. B. Chilakamarri and C. R. Mahoney, Maximal and minimal forbidden unit-distance graphs in the plane, Bulletin of the ICA, 13 (1995), 35-43.

%H Aidan Globus and Hans Parshall, <a href="https://arxiv.org/abs/1905.07829">Small unit-distance graphs in the plane</a>, [math.CO] arXiv:1905.07829, 2019.

%H Matthew McAndrews, <a href="/A059103/a059103.pdf">Simple Connected Units Distance Graphs Through 6 Vertices</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Unit-DistanceGraph.html">Unit-Distance Graph</a>

%e 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.

%Y Cf. A303792 (number of connected matchstick graphs).

%Y Cf. A308349 (number of minimal unit-distance forbidden graphs).

%K hard,more,nonn

%O 1,3

%A _David S. Newman_, Feb 13 2001

%E 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

%E a(7) from _Hans Parshall_, May 03 2018

%E a(8)-a(9) from _Hans Parshall_, May 21 2019

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Last modified June 17 22:17 EDT 2019. Contains 324200 sequences. (Running on oeis4.)