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

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• more
• nice

Comments

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.

References

• 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).

Links

• 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

Crossrefs

Cf. A066951.

Extensions

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