plantri and fullgen

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

The authors are Gunnar Brinkmann (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 1,000,000 graphs per second in many cases, so extremely large classes of graph can be exhaustively listed.

plantri (Version 5.0; January 30, 2018)

The graph classes generated by plantri include:

For more details, see the manual.


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 C and are free for all purposes other than sale for profit. However, they remain subject to our copyright and are not "public domain".

They should compile with any modern C compiler and do not need any special libraries. However, they are mostly tested under UNIX.

plantri and fullgen are distributed together as a gzipped tar file (Version 5.0).

Related papers

G. Brinkmann and B. D. McKay, Fast generation of planar graphs (expanded edition): 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: