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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 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 January 16 15:53 EST 2019. Contains 319195 sequences. (Running on oeis4.)