OFFSET
1,3
COMMENTS
K_4 can't be so drawn even though it is planar. These graphs are a subset of those counted in A046091.
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
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn,more,nice
AUTHOR
Les Reid, May 25 2002
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
STATUS
approved