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A303792 Number of connected matchstick graphs on n nodes. 1
1, 1, 2, 5, 13, 50 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
a(7) >= 211. - Eric W. Weisstein, Jan 02 2022
LINKS
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
KEYWORD
nonn,hard,more
AUTHOR
Eric W. Weisstein, Apr 30 2018
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)