plantri and fullgen

plantri and fullgen are programs for generation of certain types of planar graph.

The authors are Gunnar Brinkmann and Heidi Van den Camp (University of Ghent), and Brendan McKay (Australian National University).

Graphs are generated in such a way that exactly one member of each isomorphism class is output without the need for storing them. The speed of generation is more than 2,000,000 graphs per second in many cases, so extremely large classes of graph can be exhaustively listed.

plantri (Version 5.5; May 17, 2024)

The graph classes generated by plantri include:

For more details, see the manual. Note that version 5.2 had an error whereby some graphs could be written twice if the res/mod option was used with -q or -bp.


The program fullgen generates fullerenes, which are planar cubic graphs having only faces of size 5 or 6.

There is also an option for forbidding adjacent pentagons.

For more details, see the manual.

This version corrects an error that caused some fullerenes to be missed starting at 136 vertices, or from 254 vertices in the case of IPR fullerenes, and an error in the counts by automorphism group.

Download the programs

The programs are written in vanilla C and should compile with any modern C compiler.

plantri and fullgen are distributed together as a gzipped tar file (Version 5.5).


plantri and fullgen are copyright the authors (Brinkmann and McKay for plantri, Brinkmann for fullgen). They are subject to the Apache License, Version 2.0. You not use this software except in compliance with the License. Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "as is" basis, without warranties or conditions of any kind, either express or implied. See the License for the specific language governing permissions and limitations under the License.

Related papers

G. Brinkmann and B. D. McKay, Fast generation of planar graphs (expanded edition): MATCH Commun. Math. Comput. Chem., 58 (2007) 323-357. PDF file.

G. Brinkmann, S. Greenberg, C. Greenhill, B. D. McKay, R. Thomas and P. Wollan, Generation of simple quadrangulations of the sphere: PDF file. (Discrete Mathematics, 305 (2005) 33-54).

G. Brinkmann and B. D. McKay, Construction of planar triangulations with minimum degree 5: PDF file. (Discrete Mathematics, 301 (2005) 147-163.)

Related programs

Buckygen is another program for generating fullerenes, written by Jan Goedgebeur with input from Gunnar Brinkmann, Mahdieh Hasheminezhad, and Brendan McKay. It has fewer features than fullgen but is considerably faster. It is available here.

Thom Sulanke has written a program surftri for generating triangulations of surfaces of higher genus, including non-orientable surfaces. It is available here.

Contact the authors

Gunnar Brinkmann:
Brendan McKay: