A204198 -id:A204198 - cp's OEIS frontend

A204199 Number of (strictly) 2-connected cubic graphs on 2n nodes.

0, 0, 0, 1, 4, 24, 139, 1046, 9398, 101668, 1278335, 18248616, 290147706, 5071909933

Offset: 1

N. J. A. Sloane, Jan 12 2012

The snarkhunter program (see Links) has options "C2" and "C3" for (at least) 2- and 3-connectivity respectively. So a(n) is the difference between the outputs from "./snarkhunter X 3 n C2" and "./snarkhunter X 3 n C3", where X=2n. - Ed Wynn, Jul 22 2023

			From _Ed Wynn_, Jul 22 2023: (Start)
For n=4, the unique 8-node cubic graph that is strictly 2-connected is:
   o-o
  /| |\
 o-o o-o
  \| |/
   o-o
(End)

G. Brinkmann, J. Goedgebeur and B. D. McKay, snarkhunter.
F. C. Bussemaker, S. Cobeljic, L. M. Cvetkovic and J. J. Seidel, Computer investigations of cubic graphs, T.H.-Report 76-WSK-01, Technological University Eindhoven, Dept. Mathematics, 1976.

Cf. A002851, A204198, A364404.

a(8)-a(14) from Ed Wynn, Jul 22 2023

A364404 Number of (strictly) 1-connected cubic graphs on 2n nodes.

Original entry on oeis.org

0, 0, 0, 0, 1, 4, 29, 186, 1435, 12671, 131820, 1590900, 21940512, 339723835

Offset: 1

Ed Wynn, Jul 22 2023

			For n=5, the unique 10-node cubic graph that is strictly 1-connected is:
   o     o
  /|\   /|\
 o-o o-o o-o
  \|/   \|/
   o     o

G. Brinkmann, J. Goedgebeur and B. D. McKay, snarkhunter.

Cf. A204199, A204198, A002851.

# The snarkhunter program (see Links) has an option "C2" for (at least) 2-connectivity. So a(n) is the difference between the outputs from "./snarkhunter X 3 ns" and "./snarkhunter X 3 ns C2", where X=2n.

A199676 Number of minimally 3-connected non-isomorphic graphs on n vertices.

Original entry on oeis.org

1, 1, 3, 5, 18, 57, 285, 1513, 9824, 69536, 540622, 4494676

Offset: 4

N. J. A. Sloane, Nov 09 2011

J. P. Costalonga, R. J. Kingan, and S. R. Kingan, Constructing minimally 3-connected graphs, arXiv:2012.12059 [math.CO], 2020-2021; Algorithms 14, no. 1: 9.
Jens M. Schmidt, Combinatorial data.
David Kofoed Wind, Connected Graphs with Fewest Spanning Trees, Bachelor Thesis, Spring 2011.

Cf. A006290, A204198, A324418, A338511.

a(12) given by Jens M. Schmidt, Feb 27 2019

a(13)-a(15) from Jens M. Schmidt's web page, Jan 10 2021

A059687 Number of basic circuits of nullity n.

Original entry on oeis.org

1, 1, 1, 2, 4, 14, 57

Offset: 1

N. J. A. Sloane, Feb 06 2001

Appears to be the same as number of 3-connected cubic graphs on 2, 4, 6, 8, 10, 12 and 14 vertices. - Gordon F. Royle, Jun 02 2003

			n=2: 3 edges in parallel between 2 nodes; n=3: K_4; n=4: K_{3,3} and the trivalent graph with 6 nodes and 9 edges formed by the 1-skeleton of a triangular prism.

R. M. Foster, Geometrical circuits of electrical networks, Transactions of the American Institute of Electrical Engineers, 51 (1932), 309-317.
R. M. Foster, Topologic and algebraic considerations in network synthesis, pp. 8-18 in Proceedings of the Symposium on Modern Network Synthesis, New York, 1952, pp. 8-18. Polytechnic Institute of Brooklyn, New York, N. Y., 1952.
A. Krapez, S. K. Simic, D. V. Tosic, Parastrophically uncancellable quasigroup equations, Aequat. Math. 79 (3) (2010) 261-280 doi:10.1007/s00010-010-0016-3

Cf. A002631, A204198.

cp's OEIS Frontend

A204199 Number of (strictly) 2-connected cubic graphs on 2n nodes.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A364404 Number of (strictly) 1-connected cubic graphs on 2n nodes.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

nauty

A199676 Number of minimally 3-connected non-isomorphic graphs on n vertices.

Views

Author

Keywords

Links

Crossrefs

Extensions

A059687 Number of basic circuits of nullity n.

Views

Author

Keywords

Comments

Examples

References

Crossrefs