|
%I #19 Sep 23 2019 09:43:16
%S 0,0,0,0,0,0,1,1,6,16,59,188,685,2412,8825,32110,118505
%N Number of simple 4-regular 4-edge-connected but not 3-connected plane graphs on n nodes.
%H A. Caudron, <a href="http://sites.mathdoc.fr/PMO/PDF/C_CAUDRON_82_04.pdf">Classification des noeuds et des enlacements</a>, Public. Math. d'Orsay 82. Orsay: Univ. Paris Sud, Dept. Math., 1982.
%H S. V. Jablan, <a href="http://members.tripod.com/vismath/sl/index.html">Ordering Knots</a>
%H S. V. Jablan, L. M. Radović, and R. Sazdanović, <a href="http://eudml.org/doc/253048">Basic polyhedra in knot theory</a>, Kragujevac J. Math., 28 (2005), 155-164.
%e The first such graph has 12 nodes. It is called 12E [Jablan, Radović & Sazdanović, Fig. 2; or Caudron, p. 308c] and looks like that:
%e ___________
%e / \
%e / O---O O---O
%e |/|\ /|\ /|\ /|
%e O | O | O | O |
%e |\|/ \|/ \|/ \|
%e \ O---O O---O
%e \___________/
%Y A078666 = A007022 + this sequence.
%K nonn,more
%O 6,9
%A Slavik V. Jablan and _Brendan McKay_ Feb 06 2003
|
