**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.

The graph classes generated by **plantri** include:

- Planar triangulations
- connectivity 1, 2, 3, 4 or 5
- minimum degree 3, 4 or 5
- eulerian with connectivity 3 or 4

- Planar quadrangulations
- arbitrary simple
- 3-connected
- minimum degree 3 and simple
- 3-connected, no non-facial 4-cycles

- Planar simple graphs
- connectivity 1, 2, 3 or 4
- minimum degree 1, 2, 3, 4 or 5

- Planar simple bipartite graphs
- connectivity 1, 2 or 3
- minimum degree 1, 2, or 3

- Triangulations of a disk
- connectivity 2 or 3
- minimum degree 2 or 3

- Planar cubic graphs
- connectivity 1, 2, or 3
- connectivity 1, 2, or 3
- girth 3, 4 or 5
- cyclic connectivity 3, 4 or 5
- bipartite with cyclic connectivity 3 or 4

- Planar quartic graphs
- 3-connected simple
- 4-edge-connected simple
- 4-edge-connected
- 3-connected, 6-cyclically-edge-connected

- Appolonian triangulations

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.

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).

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.)

**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.

Gunnar Brinkmann:
Gunnar.Brinkmann@ugent.be

Brendan McKay:
bdm@cs.anu.edu.au
http://cs.anu.edu.au/~bdm