A066951 Number of nonisomorphic connected graphs that can be drawn in the plane using n unit-length edges.
1, 1, 3, 5, 12, 28, 74, 207, 633, 2008
Offset: 1
Examples
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.
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.
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
- Stefan Vogel and Mike Winkler, Matchstick Graphs Calculator (MGC), a web application for the construction and calculation of unit distance graphs and matchstick graphs.
- Eric Weisstein's World of Mathematics, Matchstick Graph
Extensions
a(7) = 70. - Jonathan Vos Post, Jan 05 2007
Corrected, extended and reference added. a(7)=74 and a(8)=207 from Read's paper. - William Rex Marshall, Nov 16 2010
a(9) from Salvia's paper added by Brendan McKay, Apr 13 2013
a(9) corrected (from version 2 [May 22 2013] of Salvia's paper) by Gaetano Ricci, May 24 2013
a(10) from Vaisse's webpage added by Raffaele Salvia, Jan 31 2015
Comments