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A000109 Number of simplicial polyhedra with n nodes; simple planar graphs with 3n-6 edges; maximal simple planar graphs; 3-connected planar triangulations; 3-connected triangulations of the sphere; 3-connected cubic planar graphs.
(Formerly M1469 N0580)
17

%I M1469 N0580

%S 1,1,1,2,5,14,50,233,1249,7595,49566,339722,2406841,17490241,

%T 129664753,977526957,7475907149,57896349553,453382272049,

%U 3585853662949,28615703421545

%N Number of simplicial polyhedra with n nodes; simple planar graphs with 3n-6 edges; maximal simple planar graphs; 3-connected planar triangulations; 3-connected triangulations of the sphere; 3-connected cubic planar graphs.

%D G. Brinkmann and Brendan McKay, in preparation. [Looking at http://users.cecs.anu.edu.au/~bdm/publications.html,there are a few papers with Brinkmann that seem relevant, in particular #126 but also #97, 81, 158. Perhaps the right one is 126.]

%D M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties. Tech. Rep. 92-91, Info. and Comp. Sci. Dept., Univ. Calif. Irvine, 1992.

%D C. F. Earl and L. J. March, Architectural applications of graph theory, pp. 327-355 of R. J. Wilson and L. W. Beineke, editors, Applications of Graph Theory. Academic Press, NY, 1979.

%D B. Gr├╝nbaum, Convex Polytopes. Wiley, NY, 1967, p. 424.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

%H David Wasserman, <a href="/A000109/b000109.txt">Table of n, a(n) for n = 3..23</a>

%H J. Bokowski and P. Schuchert, <a href="http://www.digizeitschriften.de/dms/img/?PID=GDZPPN000367230">Equifacetted 3-spheres as topes of nonpolytopal matroid polytopes</a>, Discrete Comput. Geom. 13 (1995), no. 3-4, 347-361.

%H R. Bowen and S. Fisk, <a href="/A000103/a000103.pdf">Generation of triangulations of the sphere</a> [Annotated scanned copy]

%H R. Bowen and S. Fisk, <a href="http://dx.doi.org/10.1090/S0025-5718-1967-0223277-3">Generation of triangulations of the sphere</a>, Math. Comp., 21 (1967), 250-252.

%H Gunnar Brinkmann and Brendan McKay, <a href="http://users.cecs.anu.edu.au/~bdm/plantri/">plantri and fullgen</a> programs for generation of certain types of planar graph.

%H Gunnar Brinkmann and Brendan McKay, <a href="/A000103/a000103_1.pdf">plantri and fullgen</a> programs for generation of certain types of planar graph [Cached copy, pdf file only, no active links, with permission]

%H M. Deza, M. Dutour and P. W. Fowler, <a href="http://dx.doi.org/10.1021/ci049955h">Zigzags, railroads and knots in fullerenes</a>, J. Chem. Inf. Comput. Sci., 44 (2004), 1282-1293.

%H C. F. Earl and L. J. March, <a href="/A005500/a005500_1.pdf">Architectural applications of graph theory</a>, pp. 327-355 of R. J. Wilson and L. W. Beineke, editors, Applications of Graph Theory. Academic Press, NY, 1979. (Annotated scanned copy)

%H P. J. Federico, <a href="http://dx.doi.org/10.1016/S0021-9800(69)80050-5">Enumeration of polyhedra: the number of 9-hedra</a>, J. Combin. Theory, 7 (1969), 155-161.

%H Komei Fukuda, Hiroyuki Miyata, Sonoko Moriyama, <a href="http://arxiv.org/abs/1204.0645">Complete Enumeration of Small Realizable Oriented Matroids</a>. Discrete Comput. Geom. 49 (2013), no. 2, 359--381. MR3017917. Also arXiv:1204.0645. - From _N. J. A. Sloane_, Feb 16 2013

%H R. K. Guy, <a href="/A005347/a005347.pdf">The Second Strong Law of Small Numbers</a>, Math. Mag, 63 (1990), no. 1, 3-20. [Annotated scanned copy]

%H Lee Zheng Han, Chia Vui Leong, <a href="http://archive.ymsc.tsinghua.edu.cn/pacm_download/232/8908-A5.The_Walk_of_Maximal_Planar_Graphs.pdf">The Walk of Maximal Planar Graphs</a>, 2018

%H J. Lederberg, <a href="/A000602/a000602_10.pdf">Dendral-64, II</a>, Report to NASA, Dec 1965 [Annotated scanned copy]

%H J. Lederberg, <a href="http://www.jstor.org/stable/2314879">Hamilton circuits of convex trivalent polyhedra (up to 18 vertices)</a>, Am. Math. Monthly, 74 (1967), 522-527.

%H J. Lederberg, <a href="/A000109/a000109.pdf">Hamilton circuits of convex trivalent polyhedra (up to 18 vertices)</a>, Am. Math. Monthly, 74 (1967), 522-527. (Annotated scanned copy)

%H F. H. Lutz, <a href="http://arXiv.org/abs/math.CO/0506372">Triangulated manifolds with few vertices: Combinatorial Manifolds</a>

%H G. P. Michon, <a href="http://www.numericana.com/data/polyhedra.htm">Counting Polyhedra</a>

%H I. Sciriha and P. W. Fowler, <a href="https://dx.doi.org/10.1021/ci700097j">Nonbonding Orbitals in Fullerenes: Nuts and Cores in Singular Polyhedral Graphs</a>, J. Chem. Inf. Model., 47, 5, 1763 - 1775, 2007.

%H A. Stoimenow, <a href="https://doi.org/10.1007/s00493-014-2840-x">A theorem on graph embedding with a relation to hyperbolic volume</a>, Combinatorica, October 2016, Volume 36, Issue 5, pp 557-589.

%H Thom Sulanke, <a href="http://hep.physics.indiana.edu/~tsulanke/graphs/surftri/">Generating triangulations of surfaces (surftri)</a>, (also subpages).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CubicPolyhedralGraph.html">Cubic Polyhedral Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SimplePolyhedron.html">Simple Polyhedron</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TriangulatedGraph.html">Triangulated Graph</a>

%H <a href="/index/Cor#core">Index entries for "core" sequences</a>

%Y Cf. A005964, A058378.

%K nonn,nice,hard,more,core

%O 3,4

%A _N. J. A. Sloane_

%E Extended by _Brendan McKay_ and Gunnar Brinkmann (Gunnar.Brinkmann(AT)ugent.be) using their program "plantri", Dec 19 2000

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Last modified August 19 17:41 EDT 2018. Contains 313880 sequences. (Running on oeis4.)