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A292515 Number of 4-regular 4-edge-connected planar simple graphs on n vertices. 2
0, 0, 0, 0, 0, 1, 0, 1, 1, 3, 3, 12, 19, 63, 153, 499, 1473, 4974, 16296, 56102, 192899, 674678 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

The difference between this sequence and A078666 arises because the latter lists not planar graphs but plane graphs (with the same restrictions). Among A078666(14)=64 plane graphs there is 1 pair of isomorphic graphs, namely graphs No. 63 and 64 (hereafter the enumeration of plane graphs from the LinKnot Mathematica package is used, see The Knot Atlas link), hence a(14)=64-1=63. Among 155 plane graphs on 15 vertices, the isomorphic pairs are (143, 149) and (153, 155), hence a(15)=155-2=153. The 11 isomorphic pairs of plane graphs on 16 vertices are: (456, 492), (459, 493), (464, 496), (465, 501), (466, 468), (470, 487), (473, 503), (477, 488), (478, 479), (486, 497), (498, 504).

Tuzun and Sikora say that such planar graphs constitute the set of 4-edge-connected basic Conway polyhedra, but usually it is considered that all plane graphs should be taken into account instead (see A078666 and references therein).

LINKS

Table of n, a(n) for n=1..22.

The Knot Atlas, Conway Notation.

Robert E. Tuzun and Adam S. Sikora, Verification Of The Jones Unknot Conjecture Up To 22 Crossings, arXiv:1606.06671 [math.GT] (see table 2).

CROSSREFS

Cf. A078666, A072552.

Sequence in context: A074850 A073055 A075780 * A078666 A290438 A006804

Adjacent sequences:  A292512 A292513 A292514 * A292516 A292517 A292518

KEYWORD

nonn

AUTHOR

Andrey Zabolotskiy, Sep 18 2017

STATUS

approved

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Last modified February 24 23:02 EST 2018. Contains 299629 sequences. (Running on oeis4.)