A078672 - OEIS

A078672

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

0, 0, 0, 0, 0, 0, 1, 1, 6, 16, 59, 188, 685, 2412, 8825, 32110, 118505

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OFFSET

6,9

LINKS

A. Caudron, Classification des noeuds et des enlacements, Public. Math. d'Orsay 82. Orsay: Univ. Paris Sud, Dept. Math., 1982.

S. V. Jablan, L. M. Radović, and R. Sazdanović, Basic polyhedra in knot theory, Kragujevac J. Math., 28 (2005), 155-164.

EXAMPLE

The first such graph has 12 nodes. It is called 12E [Jablan, Radović & Sazdanović, Fig. 2; or Caudron, p. 308c] and looks like that:

___________

/ \

/ O---O O---O

|/|\ /|\ /|\ /|

O | O | O | O |

|\|/ \|/ \|/ \|

\ O---O O---O

\___________/

CROSSREFS

A078666 = A007022 + this sequence.

KEYWORD

nonn,more

AUTHOR

Slavik V. Jablan and Brendan McKay Feb 06 2003

STATUS

approved