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A005470 Number of unlabeled planar simple graphs with n nodes.
(Formerly M1252)
1, 1, 2, 4, 11, 33, 142, 822, 6966, 79853, 1140916, 18681008, 333312451 (list; graph; refs; listen; history; text; internal format)



Euler transform of A003094. - Christian G. Bower


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

W. T. Trotter, ed., Planar Graphs, Vol. 9, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Amer. Math. Soc., 1993.

Turner, James; Kautz, William H. A survey of progress in graph theory in the Soviet Union. SIAM Rev. 12 1970 suppl. iv+68 pp. MR0268074 (42 #2973). See p. 19. - N. J. A. Sloane, Apr 08 2014

Vetukhnovskii, F. Ya. "Estimate of the Number of Planar Graphs." In Soviet Physics Doklady, vol. 7, pp. 7-9. 1962. - From N. J. A. Sloane, Apr 08 2014

R. J. Wilson, Introduction to Graph Theory. Academic Press, NY, 1972, p. 162.


Table of n, a(n) for n=0..12.

G. Brinkmann, and B. D. McKay, Fast generation of planar graphs, MATCH Commun. Math. Comput. Chem., 58 (2007) 323-357.

Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph.

Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph [Cached copy, pdf file only, no active links, with permission]

E. Friedman, Illustration of small graphs

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Planar Graph

Index entries for "core" sequences


a(2) = 2 since o o and o-o are the two planar simple graphs on two nodes.


A003094 = {1, 1, 1, 2, 6, 20, 99, 646, 5974, 71885, 1052805, 17449299, 313372298}; max = Length[A003094]-1; b[n_] := A003094[[n+1]]; f[x_] = (a[0]=1) + Sum[a[n]*x^n, {n, 1, max}] - Product[1/(1-x^n)^b[n], {n, 1, max}]; sf = Series[f[x], {x, 0, max}] // CoefficientList[#, x]&; Table[a[n], {n, 0, max}] /. Solve[Thread[sf == 0]][[1]] (* Jean-Fran├žois Alcover, Apr 25 2013, after Christian G. Bower *)


Cf. A003094 (connected planar graphs), A034889, A039735 (planar graphs by nodes and edges).

Cf. A126201.

Sequence in context: A123469 A123448 A039707 * A123471 A123416 A123406

Adjacent sequences:  A005467 A005468 A005469 * A005471 A005472 A005473




N. J. A. Sloane


n=8 term corrected and n=9..11 terms calculated by Brendan McKay

Terms a(0) - a(10) confirmed by David Applegate and N. J. A. Sloane, Mar 09 2007

a(12) added by Vaclav Kotesovec after A003094 (computed by Brendan McKay), Dec 06 2014



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Last modified January 17 16:47 EST 2018. Contains 297822 sequences.