In `Sage`

, see `www.sagemath.org`

, you find the algorithm

G. Brinkmann and B.D. McKay, *Fast generation of planar graphs*, MATCH-Communications in Mathematical and in Computer Chemistry, 58(2):323-357, 2007.

implemented, for which the optional package `plantri`

needs to be installed. From the documentation:

```
An iterator over connected planar graphs using the plantri generator.
This uses the plantri generator (see [plantri]_) which is available
through the optional package plantri.
.. NOTE::
The non-3-connected graphs will be returned several times, with all
its possible embeddings.
```

Here are a few tests:

```
sage: %time len(list(graphs.planar_graphs(4)))
CPU times: user 3.23 ms, sys: 7.93 ms, total: 11.2 ms
Wall time: 21.6 ms
6
sage: %time len(list(graphs.planar_graphs(5)))
CPU times: user 11.9 ms, sys: 8.35 ms, total: 20.3 ms
Wall time: 31.9 ms
25
sage: %time len(list(graphs.planar_graphs(6)))
CPU times: user 72.5 ms, sys: 11.7 ms, total: 84.2 ms
Wall time: 96.3 ms
179
sage: %time len(list(graphs.planar_graphs(7)))
CPU times: user 920 ms, sys: 67.3 ms, total: 988 ms
Wall time: 1 s
2014
sage: %time len(list(graphs.planar_graphs(8)))
CPU times: user 19.6 s, sys: 914 ms, total: 20.5 s
Wall time: 20.6 s
31178
```