A003055 - OEIS

%I M2464 #46 Jan 01 2022 13:16:26

%S 1,1,3,5,10,19,39,84,196,479

%N Number of connected graphs, up to homeomorphism, that can be drawn in the plane using unit-length edges.

%C K_4 can't be so drawn even though it is planar. Although a square with a tail of length 1 and a triangle with a tail of length 2 are nonisomorphic graphs with five edges, they are homeomorphic as topological spaces.

%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.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MatchProblem.html">Match Problem</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Matchstick_graph">Matchstick graph</a>

%Y Cf. A066951.

%K nonn,more,nice

%O 1,3

%A _N. J. A. Sloane_

%E Corrected by _Brendan McKay_ and _Les Reid_ (les(AT)math.smsu.edu), May 25 2002

%E Reference and a(8) from Read's paper added by _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 5 [Jan 05 2015] of Salvia's paper; a(10) from Vaisse's webpage added by _Raffaele Salvia_, Jan 31 2015