A planar connected graph is a graph which is both planar and connected. The numbers of planar connected
simple graphs, counted up to graph
isomorphism, with 
, 2, ... vertices
are 1, 1, 2, 6, 20, 99, 646, 5974, 71885, ... (OEIS A003094;
Steinbach 1990, p. 131). The finite simple graphs
that are planar and 3-connected
are precisely the polyhedral graphs.
The following table gives the numbers of planar connected graphs having minimum degrees of at least 
.
 | OEIS |  , 2, 3, ... |
| 2 | A054381 | 0, 0, 1, 3, 10, 49, 332, ... |
The numbers of planar connected graphs with 
, 2, ... edges
are 1, 1, 3, 5, 12, 30, 79, 227, 709, 2318, ... (OEIS A046091).
