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%I #20 Apr 12 2019 14:08:49
%S 1,1,2,8,2,2,3,4,3
%N Number of cubic graphs with minimal crossing number n and the minimal possible number of vertices.
%C a(0) = 1 from the complete graph K_4.
%C a(1) = 1 from the utility graph K_{3,3}.
%C a(2) = 2 from the Petersen graph (and 1 other).
%C a(3) = 8 from the Heawood graph, GP(7,2) (and 6 others).
%C a(4) = 2 from the Moebius-Kantor and 8-crossed prism graphs.
%C a(5) = 2 from the Pappus graph (and 1 other).
%C a(6) = 3 from the Desargues graph (and 2 others based on 10_3 configurations).
%C a(7) = 4 from the 7-crossing graphs (4 in total).
%C a(8) = 3 from the McGee and Nauru graphs (and 1 other).
%C a(9) >= 3 from GP(13,5), the Coxeter-1, and McGee+1 graphs (and unknown others). - _Eric W. Weisstein_, Apr 12 2019
%C a(10) >= 2 from the Levi-1 (=McGee+2) graph and graph from 2019 Clancy et al. preprint (and unknown others). - _Eric W. Weisstein_, Apr 12 2019
%C a(11) >= 1 from the Coxeter graph (and unknown others).
%C a(13) >= 1 from the Levi graph (and unknown others).
%H A. E. Brouwer, <a href="http://www.win.tue.nl/~aeb/drg/graphs/Heawood.html">The Heawood Graph</a>
%H Geoff Exoo, <a href="https://web.archive.org/web/20190119121623/http://isu.indstate.edu/ge/COMBIN/RECTILINEAR/">Rectilinear Drawings of Famous Graphs</a>
%H Michael Haythorpe and Alex Newcombe, <a href="https://arxiv.org/abs/1804.10336">There are no Cubic Graphs on 26 Vertices with Crossing Number 11</a>, arXiv preprint arXiv:1804.10336 [math.CO], 2018.
%H Ed Pegg, Jr., <a href="http://www.maa.org/editorial/mathgames/mathgames_12_29_03.html">Cubic Symmetric Graphs</a>
%H Ed Pegg, Jr., <a href="http://mathworld.wolfram.com/CubicSymmetricGraph.html">Cubic Symmetric Graphs</a>
%H Ed Pegg, Jr., <a href="/A110507/a110507.png">Heawood graph shown with crossing number 3 and more symmetrically</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SmallestCubicCrossingNumberGraph.html">Smallest Cubic Crossing Number Graph</a>
%Y Cf. A110507.
%K nonn,more
%O 0,3
%A _Ed Pegg Jr_, Apr 08 2019
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