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Number of simple 4-regular 4-edge-connected but not 3-connected plane graphs on n nodes.
2

%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