A072552 - OEIS

A072552

Number of connected planar regular graphs of degree 4 with n nodes.

1, 0, 1, 1, 3, 3, 13, 21, 68, 166, 543, 1605, 5413, 17735, 61084, 210221, 736287

(list; graph; refs; listen; history; text; internal format)

OFFSET

6,5

COMMENTS

Numbers were obtained using the graph generator GENREG in combination with a test for planarity implemented by M. Raitner.

LINKS

Markus Meringer, GENREG

Markus Meringer, GenReg, Generation of regular graphs.

M. Raitner, Test for planarity [broken link]

Robert E. Tuzun and Adam S. Sikora, Verification Of The Jones Unknot Conjecture Up To 22 Crossings, Journal of Knot Theory and Its Ramifications (2018) 1840009, arXiv:1606.06671 [math.GT], 2016-2020 (see table 2).

EXAMPLE

From Allan Bickle, May 13 2024: (Start)

For n=6, the unique graph is the octahedron.

For n=8, the unique graph is the square of an 8-cycle.

For n=9, the unique graph is the dual of the Herschel graph. (End)

CROSSREFS

Cf. A005964, A006820, A078666, A292515 (4-edge-connected graphs only).

Cf. A007022, A111361 (other 4-regular planar graphs).

KEYWORD

nonn,more

AUTHOR

Markus Meringer (meringer(AT)uni-bayreuth.de), Aug 05 2002

EXTENSIONS

a(19)-a(22) from Andrey Zabolotskiy, Mar 21 2018 from Tuzun & Sikora.

STATUS

approved