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A003055 Number of connected graphs, up to homeomorphism, that can be drawn in the plane using unit-length edges.
(Formerly M2464)
1, 1, 3, 5, 10, 19, 39, 84, 196, 479 (list; graph; refs; listen; history; text; internal format)



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.


M. Gardner, The Unexpected Hanging and Other Mathematical Diversions. Simon and Schuster, NY, 1969, p. 80.

R. C. Read, From Forests to Matches, Journal of Recreational Mathematics, Vol. 1:3 (Jul 1968), 60-172.

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


Table of n, a(n) for n=1..10.

Jean-Paul Delahaye, Les graphes-allumettes, (in French), Pour la Science no. 445, November 2014.

Raffaele Salvia, A catalogue of matchstick graphs, arXiv:1303.5965 [math.CO], 2013-2015.

Alexis Vaisse, Matchstick graphs

Eric Weisstein's World of Mathematics, Match Problem.

Wikipedia, Matchstick graph


Cf. A066951.

Sequence in context: A238431 A014610 A117591 * A317766 A217925 A018101

Adjacent sequences:  A003052 A003053 A003054 * A003056 A003057 A003058




N. J. A. Sloane


Corrected by Brendan McKay and Les Reid (les(AT)math.smsu.edu), May 25 2002

Reference and a(8) from Read's paper added by William Rex Marshall, Nov 16 2010

a(9) from Salvia's paper added by Brendan McKay, Apr 13 2013

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



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Last modified February 29 09:35 EST 2020. Contains 332355 sequences. (Running on oeis4.)