a(7) >= 209.
Table of n, a(n) for n=1..6.
Eric Weisstein's World of Mathematics, Connected Graph
Eric Weisstein's World of Mathematics, Matchstick Graph
a(6) = A059103(6) - 1.
a(n) <= A059103(n).
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 appear to be 13 connected graphs on 7 nodes that are unit-distance but non-matchstick (including Y_3+e and the Moser spindle).
Sequence in context: A269068 A098716 A082938 * A059103 A260709 A112836
Adjacent sequences: A303789 A303790 A303791 * A303793 A303794 A303795
Eric W. Weisstein, Apr 30 2018