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%I #61 Feb 20 2024 10:33:47
%S 1,1,3,5,12,28,74,207,633,2008
%N Number of nonisomorphic connected graphs that can be drawn in the plane using n unit-length edges.
%C K_4 can't be so drawn even though it is planar. These graphs are a subset of those counted in A046091.
%D M. Gardner, The Unexpected Hanging and Other Mathematical Diversions. Simon and Schuster, NY, 1969, p. 80.
%D R. C. Read, From Forests to Matches, Journal of Recreational Mathematics, Vol. 1:3 (Jul 1968), 60-172.
%H Jean-Paul Delahaye, <a href="http://www.pourlascience.fr/ewb_pages/a/article-les-graphes-allumettes-33448.php">Les graphes-allumettes</a>, (in French), Pour la Science no. 445, November 2014.
%H Raffaele Salvia, <a href="http://arxiv.org/abs/1303.5965">A catalogue of matchstick graphs</a>, arXiv:1303.5965 [math.CO], 2013-2015.
%H Alexis Vaisse, <a href="http://alexis.vaisse.monsite-orange.fr/page-54b81c6bc01a2.html">Matchstick graphs</a>
%H Stefan Vogel and Mike Winkler, <a href="https://mikematics.de/matchstick-graphs-calculator.htm">Matchstick Graphs Calculator (MGC)</a>, a web application for the construction and calculation of unit distance graphs and matchstick graphs.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MatchstickGraph.html">Matchstick Graph</a>
%e Up to five edges, every planar graph can be drawn with edges of length 1, so up to this point the sequence agrees with A046091 (connected planar graphs with n edges) [except for the fact that that sequence begins with no edges]. For six edges, the only graphs that cannot be drawn with edges of length 1 are K_4 and K_{3,2}. According to A046091, there are 30 connected planar graphs with 6 edges, so the sixth term is 28.
%Y Cf. A003055, A002905, A046091.
%K nonn,more,nice
%O 1,3
%A _Les Reid_, May 25 2002
%E a(7) = 70. - _Jonathan Vos Post_, Jan 05 2007
%E Corrected, extended and reference added. a(7)=74 and a(8)=207 from Read's paper. - _William Rex Marshall_, Nov 16 2010
%E a(9) from Salvia's paper added by _Brendan McKay_, Apr 13 2013
%E a(9) corrected (from version 2 [May 22 2013] of Salvia's paper) by _Gaetano Ricci_, May 24 2013
%E a(10) from Vaisse's webpage added by _Raffaele Salvia_, Jan 31 2015
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