# Planar graphs

This page contains graphs and counts of various planar graph classes. All of these graphs and numbers were obtained by the program plantri, except the counts for connected planar graphs which were obtained by the program geng.

The graph lists available in 'planar_code' or 'graph6' format. The larger files are compressed with gzip.

The following lists are available:

For fullerenes, see the Fullerenes page.

Some additional lists of planar graphs can be found on Brendan McKay's planar graph page.

Plantri can generate much more graph classes than the ones listed on this page (e.g. planar graphs with a given minimum degree or with connectivity requirements). For a complete list of the graph classes which can be generated with this program, see the plantri page.

### Connected planar graphs

The table below lists the number of non-isomorphic connected planar graphs. Note that isomorphism is considered according to the abstract graphs regardless of their embedding. So graphs which can be embedded in multiple ways only appear once in the lists. If you are looking for plane graphs which are not isomorphic as embedded graphs, we refer to the plantri-page.

Vertices No. of graphs
11
21
32
46
520
699
7646
85974
971885
101052805
1117449299
12313372298

### 3-connected planar triangulations

Note that the dual graph of a 3-connected planar triangulation is a cubic polyhedron (i.e. a cubic 3-connected simple planar graph).

Vertices No. of graphs
4 1
5 1
6 2
7 5
8 14
9 50
10 233
11 1249
12 7595
13 49566
14 339722
15 2406841
16 17490241
17 129664753
18 977526957
19 7475907149
20 57896349553
21 453382272049
22 3585853662949
23 28615703421545

### 3-connected planar triangulations of a disk

Vertices No. of graphs
41
52
67
727
8132
9773
105017
1134861
12253676
131903584
1414616442
15114254053
16906266345
177277665889
1859066524810
19483864411124
203996427278475
2133250623548406

### 3-connected planar simple graphs (i.e. convex polytopes)

Vertices No. of graphs
41
52
67
734
8257
92606
1032300
11440564
126384634
1396262938
141496225352
1523833988129
16387591510244
176415851530241
18107854282197058

Vertices No. of graphs
81
90
101
111
123
133
1411
1518
1658
17139
18451
191326
204461
2114554
2249957
23171159
24598102
252098675
267437910
2726490072
2894944685
29341867921
301236864842
314493270976
3216387852863
3359985464681
34220320405895
35811796327750
363000183106119

### 3-connected planar self-dual graphs

Vertices No. of graphs
41
51
62
76
816
950
10165
11554
121908
136667
1423556
1584048
16302404
171095536
183993623