
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)=641=63. Among 155 plane graphs on 15 vertices, the isomorphic pairs are (143, 149) and (153, 155), hence a(15)=1552=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 4edgeconnected basic Conway polyhedra, but usually it is considered that all plane graphs should be taken into account instead (see A078666 and references therein).
