Last update = Apr 24, 2018.
Groups & Graphs
      is a software package for graphs, digraphs, graph embeddings, projective configurations, polyhedra, convex hulls, combinatorial designs, automorphism groups, fractals, and more.

An updated list of torus maps is available.

Andrew Chalaturnyk's Hamilton Cycle code is available. This is C-code under the GNU licence which compiles to a unix tool to find hamilton cycles very fast. Go to the Downloads page.


Current versions

Groups & Graphs 3.6.0 for OS X.
G&G requires the Carbon environment in OSX. This is available in OSX 10.8 (Mountain Lion). It is not supported in OSX 10.12 (Sierra). I will not port this code to Apple's Cocoa environment. Development has continued in C++, in the unix-like Haiku OS.

Click for info on using G&G. The overview contains sample windows for graphs, digraphs, groups, torus maps, projective maps, sphere maps, projective configurations, polyhedra, and fractals. It also contains pictures of some interesting graphs. Sources of information for some of the algorithms are also available.

Windows or Linux users: G&G is not available for MS Windows or Linux. However many computers that run Windows or Linux can also run Haiku . See the G&G Haiku page.

G&G_Haiku can also be run in a Haiku virtual box in OSX, Windows, or Linux.


Graph Theory Textbook

Many of the algorithms used by G&G are described in the textbook Graphs, Algorithms, and Optimization by William Kocay and Donald L. Kreher, Chapman & Hall/CRC Press, Boca Raton, 2005. The second edition (2016) is now available. It is available from


Some Features of G&G
  • Visual graph/digraph editor;
  • Automorphism group;
  • Graph isomorphism algorithm;
  • Graph embeddings in the plane, sphere, torus, and projective plane;
  • Hamiltonian cycles, planarity test, planar layout, torus maps, sphere maps, projective maps;
  • Line graphs, inverse line graphs, neighbour graphs, bipartite doubles, distance-k graphs, antipodal graphs;
  • Orbits, generators, elements of permutation groups;
  • Block systems, commutator subgroups, stabilisers, quotient groups, Sylow subgroups;
  • Cayley graphs, double cosets, normalizers, centralizers;
  • Point-line configurations in the real projective plane;
  • 3D and 4D Polyhedra, Convex Hulls;
  • Fractals -- Julia sets and the Mandelbrot set;
  • n-Body simulations;


This page has been visited times since May 25, 2007.

icon   Go to Bill Kocay's Home Page.