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Number of connected matchstick graphs on n nodes.
1

%I #20 Feb 16 2025 08:33:54

%S 1,1,2,5,13,50

%N Number of connected matchstick graphs on n nodes.

%C a(7) >= 211. - _Eric W. Weisstein_, Jan 02 2022

%H Jaskaran Singh Grover, Changliu Liu and Katia Sycara, <a href="http://robotics.cs.rutgers.edu/wafr2020/wp-content/uploads/sites/7/2020/05/WAFR_2020_FV_36.pdf">Deadlock Analysis and Resolution for Multi-Robot Systems</a>, (2020).

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

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

%F a(6) = A059103(6) - 1.

%F a(n) <= A059103(n).

%e 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.

%e There are 11 connected graphs on 7 nodes that are unit-distance but non-matchstick (including Y_3+e and the Moser spindle).

%Y Cf. A059103.

%K nonn,hard,more,changed

%O 1,3

%A _Eric W. Weisstein_, Apr 30 2018