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A066951 Number of nonisomorphic connected graphs that can be drawn in the plane using n unit-length edges. 3
1, 1, 3, 5, 12, 28, 74, 207, 633, 2008 (list; graph; refs; listen; history; text; internal format)



K_4 can't be so drawn even though it is planar. These graphs are a subset of those counted in A046091.


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.


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

Stefan Vogel and Mike Winkler, Matchstick Graphs Calculator (MGC), a CAS for the construction and calculation of matchstick graphs.

Eric Weisstein's World of Mathematics, Match Problem


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.


Cf. A003055, A002905, A046091.

Sequence in context: A005913 A056690 A317580 * A295065 A046091 A002905

Adjacent sequences:  A066948 A066949 A066950 * A066952 A066953 A066954




Les Reid, May 25 2002


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



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Last modified May 26 13:49 EDT 2020. Contains 334626 sequences. (Running on oeis4.)