A005470 Number of unlabeled planar simple graphs with n nodes.

1, 1, 2, 4, 11, 33, 142, 822, 6966, 79853, 1140916, 18681008, 333312451

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• core
• nice
• hard
• more

Comments

Euler transform of A003094. - Christian G. Bower

Examples

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

References

• 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.

Links

• 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

Crossrefs

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

Cf. A126201.

Programs

Mathematica

A003094 = Cases[Import["https://oeis.org/A003094/b003094.txt", "Table"], {, }][[All, 2]];
(* EulerTransform is defined in A005195 *)
EulerTransform[Rest @ A003094] (* Jean-François Alcover, Apr 25 2013, updated Mar 17 2020 *)

Extensions

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