G&G Graph Library

Last update=6 Feb, 2009

A number of graph files are available via ftp. See also the G & G overview, where pictures of many of these graphs are shown. If you have interesting graphs/digraphs/groups, please consider posting them on this website. Examples are strongly regular graphs, distance regular graphs, incidence graphs of finite geometries or BIBDs, catalogs of cubic graphs, quartic graphs, torus maps, transitive graphs, etc. Send them by e-mail, together with any additional information that may be useful.

The Macintosh and Windows versions of G&G can now read and write the same files. The files are stored as self-extracting stuffit archives. Graphs can be downloaded in G&G binary format and in G&G text format. Locate to the anonymous ftp server to download them in text format. Use your e-mail address as your password.

The "Draw Symmetric" command in G & G can be used to produce interesting drawings of graphs. Click for an example illustrating 4 very different-looking symmetric views of Q4, the 4-cube.

## G&G text format for graphs

Graphs are stored in a standard text format. The graph of the cube is used as an example.

&Graph
Cube
8
-1 2 4 5
-2 3 6
-3 4 7
-4 8
-5 6 8
-6 7
-7 8
0

The first line indicates that a graph follows. The second line is the name of the graph. The third line is the number n of vertices. The vertices are numbered 1..n. Vertex 1 is indicated by -1. Its adjacent points follow. Vertex 2 is indicated by -2, then its adjacent points, etc. The end of the list is indicated by 0.

Graphs in this format are very easily input.

read(u)
while u<0 begin
u = -u
read(v)
while v>0 begin
AddEdge(u,v)
read(v)
end
u = v
end

The graph adjacencies can be followed by the (h,v)-coordinates of the vertices. These are the horizontal and vertical offsets (integers) from the top left corner of the window. For the example above, coordinates appear as follows.

&Coordinates of vertices:
-1 211 14
-2 301 14
-3 301 89
-4 211 89
-5 146 74
-6 236 74
-7 236 149
-8 146 149

Additional optional information can also be included, such as the colour of the vertices, and a renaming of the points. Save some graphs in text format using G&G to see the format used.

## Download:

The Vertex-Transitive Graphs up to 17 vertices.

The connected cubic graphs on 10 points (submitted by R. Figuero)

4 views of the Petersen graph, and 4 views of Q4, the 4-cube

The Platonic polyhedra

• Tetrahedron, cube, octahedron, dodecahedron, icosahedron, and their line graphs and truncations

The strongly regular graphs of degree 12 on 25 vertices

Some strongly regular graphs

• Schlafli, Shrikhande, Clebsch, Hoffman-Singleton graphs, and 2 graphs on 26 points

Incidence graphs of some projective planes

• PG(2,2), PG(2,3), PG(2,4), PG(2,5), PG(2,7), PG(2,8), PG(2,9) and the Hall and Hughes planes of order 9

Some non-hamiltonian graphs

• Grinberg, Thomassen, Tutte, Coxeter (2 views), Horton graphs.
The Grinberg and Tutte graphs are planar, 3-regular, 3-connected, non-hamiltonian graphs. The Horton and Thomassen graphs are hypotraceable -- ie, they have no hamilton path, but if any vertex is deleted, there is a hamilton path. The Coxeter graph has an automorphism mapping any 3-path to any 3-path.

Some of the cages -- (3,5), (3,6), (3,7), (3,8), (4,5), (4,6), etc.

• A (k,n)-cage is a minimal graph of degree k, with a smallest cycle of length n.

A number of other miscellaneous graphs are available. Locate to the ftp server to download them.

Back to the Groups & Graphs home page.