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

%I #34 May 14 2024 00:46:35

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

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

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

%H Markus Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">GENREG</a>

%H Markus Meringer, <a href="https://sourceforge.net/projects/genreg/">GenReg</a>, Generation of regular graphs.

%H Markus Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">Tables of Regular Graphs</a>

%H M. Raitner, <a href="http://www.infosun.fmi.uni-passau.de/GTL/">Test for planarity</a> [broken link]

%H Robert E. Tuzun and Adam S. Sikora, <a href="https://doi.org/10.1142/S0218216518400096">Verification Of The Jones Unknot Conjecture Up To 22 Crossings</a>, Journal of Knot Theory and Its Ramifications (2018) 1840009, <a href="https://arxiv.org/abs/1606.06671">arXiv:1606.06671</a> [math.GT], 2016-2020 (see table 2).

%e From _Allan Bickle_, May 13 2024: (Start)

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

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

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

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

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

%K nonn,more

%O 6,5

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

%E a(19)-a(22) from _Andrey Zabolotskiy_, Mar 21 2018 from Tuzun & Sikora.