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, 437526, 1624492, 6043496, 22553387, 84345031, 316183706, 1187740914, 4471145942, 16864755973, 63737132585, 241337964503, 915500561602

Offset

6,9

Links

Table of n, a(n) for n=6..34.

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

S. V. Jablan, Ordering Knots

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

Formula

a(n) = A078666(n) - A007022(n).

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

Cf. A007022, A078666.

Sequence in context: A389889 A091649 A125628 * A219817 A120795 A118640

Adjacent sequences: A078669 A078670 A078671 * A078673 A078674 A078675

Keyword

nonn,more,changed

Author

Slavik V. Jablan and Brendan McKay, Feb 06 2003

Extensions

a(23)-a(34) from Sean A. Irvine, Jul 09 2025

Status

approved