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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. 1
1, 1, 2, 5, 13, 51 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

The existence of a simple, connected, unit-distance graph that is n-colorable, 5<=n<=7, will raise the lower bound on X(R^2) from 4, the current lower bound, to n. The upper bound is 7, so should a 7-colorable, simple, connected, unit-distance graph be found, the chromatic number of the plane problem will be solved. - Matthew McAndrews, Feb 21 2016

LINKS

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

Matthew McAndrews, Simple Connected Units Distance Graphs Through 6 Vertices

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

Sequence in context: A269068 A098716 A082938 * 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

STATUS

approved

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Last modified February 20 01:17 EST 2018. Contains 299357 sequences. (Running on oeis4.)