cp's OEIS Frontend

A111361 The number of 4-regular plane graphs with n vertices with all faces 3-gons or 4-gons.

%I A111361 #32 Jan 25 2025 20:00:34
%S A111361 0,0,0,0,1,0,1,1,2,1,5,2,8,5,12,8,25,13,30,23,51,33,76,51,109,78,144,
%T A111361 106,218,150,274,212,382,279,499,366,650,493,815,623,1083,800,1305,
%U A111361 1020,1653,1261,2045,1554,2505,1946,3008,2322,3713,2829,4354,3418,5233,4063,6234
%N A111361 The number of 4-regular plane graphs with n vertices with all faces 3-gons or 4-gons.
%C A111361 These are the 4-regular graphs corresponding to the 3-regular fullerenes. Only the two smallest possible face sizes are allowed. The numbers up to a(33) have been checked by 2 independent programs. Further numbers have not been checked independently.
%H A111361 Andrey Zabolotskiy, <a href="/A111361/b111361.txt">Table of n, a(n) for n = 2..131</a> (from Hasheminezhad & McKay)
%H A111361 G. Brinkmann, O. Heidemeier and T. Harmuth, <a href="https://doi.org/10.1016/S0166-218X(02)00549-8">The construction of cubic and quartic planar maps with prescribed face degrees</a>, Discrete Applied Mathematics 128: 541-554, (2003).
%H A111361 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 A111361 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 A111361 Michel-Marie Deza, Mathieu Dutour Sikiric and Mikhail Ivanovitch Shtogrin, <a href="https://doi.org/10.1007/978-81-322-2449-5">Geometric Structure of Chemistry-Relevant Graphs</a>, Springer, 2015; see Sec. 4.4.
%H A111361 Mathieu Dutour Sikiric and Michel Deza, <a href="https://arxiv.org/abs/0910.5323">4-regular and self-dual analogs of fullerenes</a>, arXiv:0910.5323 [math.GT], 2009.
%H A111361 Mahdieh Hasheminezhad and Brendan D. McKay, <a href="https://doi.org/10.7151/dmgt.1482">Recursive generation of simple planar quadrangulations with vertices of degree 3 and 4</a>, Discussiones Mathematicae Graph Theory, 30 (2010), 123-136.
%H A111361 T. Tarnai, F. Kovács, P. W. Fowler and S. D. Guest, <a href="https://doi.org/10.1098/rspa.2012.0116">Wrapping the cube and other polyhedra</a>, Proc. Roy. Soc. A 468(2145) (2012), 2652-2666. DOI: 10.1098/rspa.2012.0116.
%e A111361 From _Allan Bickle_, May 13 2024: (Start)
%e A111361 The smallest example (n=6) is the octahedron (only 3-gons).
%e A111361 For n=8, the unique graph is the square of an 8-cycle.
%e A111361 For n=9, the unique graph is the dual of the Herschel graph. (End)
%Y A111361 Cf. A007894.
%Y A111361 Cf. A167156, A167157, A167158, A167159.
%Y A111361 Cf. A007022, A072552, A078666, A292515 (4-regular planar graphs with restrictions).
%K A111361 nonn
%O A111361 2,9
%A A111361 _Gunnar Brinkmann_, Nov 07 2005
%E A111361 Leading zeros prepended, terms a(34) and beyond added from the book by Deza et al. (except for a(60) from the paper by Brinkmann et al.) by _Andrey Zabolotskiy_, Oct 09 2021