cp's OEIS Frontend

A003055 Number of connected graphs, up to homeomorphism, that can be drawn in the plane using unit-length edges.

%I A003055 M2464 #47 Feb 16 2025 08:32:27
%S A003055 1,1,3,5,10,19,39,84,196,479
%N A003055 Number of connected graphs, up to homeomorphism, that can be drawn in the plane using unit-length edges.
%C A003055 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 A003055 M. Gardner, The Unexpected Hanging and Other Mathematical Diversions. Simon and Schuster, NY, 1969, p. 80.
%D A003055 R. C. Read, From Forests to Matches, Journal of Recreational Mathematics, Vol. 1:3 (Jul 1968), 60-172.
%D A003055 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003055 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 A003055 Raffaele Salvia, <a href="http://arxiv.org/abs/1303.5965">A catalogue of matchstick graphs</a>, arXiv:1303.5965 [math.CO], 2013-2015.
%H A003055 Alexis Vaisse, <a href="http://alexis.vaisse.monsite-orange.fr/page-54b81c6bc01a2.html">Matchstick graphs</a>
%H A003055 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MatchProblem.html">Match Problem</a>
%H A003055 Wikipedia, <a href="http://en.wikipedia.org/wiki/Matchstick_graph">Matchstick graph</a>
%Y A003055 Cf. A066951.
%K A003055 nonn,more,nice
%O A003055 1,3
%A A003055 _N. J. A. Sloane_
%E A003055 Corrected by _Brendan McKay_ and _Les Reid_ (les(AT)math.smsu.edu), May 25 2002
%E A003055 Reference and a(8) from Read's paper added by _William Rex Marshall_, Nov 16 2010
%E A003055 a(9) from Salvia's paper added by _Brendan McKay_, Apr 13 2013
%E A003055 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