A003094 Number of unlabeled connected planar simple graphs with n nodes.
1, 1, 1, 2, 6, 20, 99, 646, 5974, 71885, 1052805, 17449299, 313372298, 5942258308
Offset: 0
Examples
a(3) = 2 since the path o-o-o and the triangle are the two connected planar simple graphs on three nodes.
References
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- R. J. Wilson, Introduction to Graph Theory, Academic Press, NY, 1972, p. 162.
Links
- David Wasserman, Brendan McKay and Georg Grasegger, Table of n, a(n) for n = 0..13
- Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018.
- E. Friedman, Illustration of small graphs
- Brendan McKay, Planar graphs
- N. J. A. Sloane, Transforms
- Peter Steinbach, Field Guide to Simple Graphs, Volume 1, Part 17 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)
- Eric Weisstein's World of Mathematics, Planar Connected Graph
Programs
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Mathematica
a[n_Integer?NonNegative] := a[n] = Module[{m, s, g}, s = Subsets[Range[n], {2}]; m = Length[s]; g = Graph[Range[n], UndirectedEdge @@@ #] & /@ (Pick[s, #, 1] & /@ (IntegerDigits[#, 2, m] & /@ Range[0, 2^m - 1])); Length[DeleteDuplicates[Select[Select[g, ConnectedGraphQ], PlanarGraphQ], IsomorphicGraphQ]]]; Table[a[n], {n, 0, 6}] (* Robert P. P. McKone, Oct 14 2023 *) -
nauty
geng -c $n | planarg -q | countg -q # Georg Grasegger, Jul 06 2023
Extensions
More terms from Brendan McKay
a(12) added by Brendan McKay, Dec 06 2014
a(13) added by Georg Grasegger, Jul 06 2023
Comments