Version 0.5

Author: wilfwilson

README.md

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+# README #
+## digraphs-lib ##
+### Library of digraphs for the Digraphs package of GAP ###
+
+
+
+In this directory is a collection of various types of digraphs, which can be
+loaded into the GAP computational algebra system using the [Digraphs
+package](http://www-circa.mcs.st-and.ac.uk/~jamesm/digraphs.php).  It is a
+completely optional addition to the package, which can be used to produce
+examples of digraphs for use in the package.
+
+
+
+Getting digraphs-lib
+--------------------
+The latest version of this library is available at the following link:
+
+https://bitbucket.org/james-d-mitchell/digraphs/downloads
+
+Simply download it and extract the archive into the root directory of your
+Digraphs installation.  This should result in a `digraphs-lib` directory inside
+your `digraphs` directory.
+
+
+
+Using digraphs-lib
+------------------
+Once the library is installed, simply launch GAP, load the Digraphs package, and
+use the `ReadDigraphs` function on one of the files in the `digraph-lib`
+directory.  This will return a list of digraphs which can be used as required.
+
+Here is an example GAP session:
+
+```
+gap> LoadPackage("digraphs", false);;
+gap> filename := "~/gap/pkg/digraphs/digraphs-lib/latin.g6.gz";;
+gap> latin_graphs := ReadDigraphs(filename);
+[ <digraph with 100 vertices, 2700 edges>,
+  <digraph with 121 vertices, 3630 edges>,
+  <digraph with 144 vertices, 4752 edges>,
+  <digraph with 169 vertices, 6084 edges>,
+  <digraph with 196 vertices, 7644 edges>,
+  <digraph with 225 vertices, 9450 edges>,
+  <digraph with 256 vertices, 11520 edges>,
+  <digraph with 289 vertices, 13872 edges>,
+  <digraph with 324 vertices, 16524 edges>,
+  <digraph with 361 vertices, 19494 edges>,
+  <digraph with 4 vertices, 12 edges>,
+  <digraph with 400 vertices, 22800 edges>,
+  <digraph with 441 vertices, 26460 edges>,
+  <digraph with 484 vertices, 30492 edges>,
+  <digraph with 529 vertices, 34914 edges>,
+  <digraph with 576 vertices, 39744 edges>,
+  <digraph with 625 vertices, 45000 edges>,
+  <digraph with 676 vertices, 50700 edges>,
+  <digraph with 729 vertices, 56862 edges>,
+  <digraph with 784 vertices, 63504 edges>,
+  <digraph with 841 vertices, 70644 edges>,
+  <digraph with 9 vertices, 54 edges>,
+  <digraph with 900 vertices, 78300 edges>,
+  <digraph with 16 vertices, 144 edges>,
+  <digraph with 25 vertices, 300 edges>,
+  <digraph with 36 vertices, 540 edges>,
+  <digraph with 49 vertices, 882 edges>,
+  <digraph with 64 vertices, 1344 edges>,
+  <digraph with 81 vertices, 1944 edges> ]
+```
+
+
+
+Types of digraph available
+--------------------------
+The following files were created by the authors of the Digraphs package:
+
+  * `acyclic.ds6.gz` - Acyclic graphs
+  * `complete.g6.gz` - Complete graphs
+  * `cyclic.ds6.gz` - Cyclic graphs
+  * `empty.s6` - Empty graphs (graphs with no edges)
+  * `extreme.d6.gz` - Required for DigraphsTestExtreme
+  * `extreme.ds6.gz` - Required for DigraphsTestExtreme
+  * `multi.ds6.gz` - Multigraphs
+  * `random.d6.gz` - A few randomly generated digraphs
+  * `sparse.ds6.gz` - Sparse graphs (few edges per vertex)
+  * `tournament.d6.gz` - Tournaments
+
+The following files contain symmetric graphs taken from the [nauty and Traces
+website](http://pallini.di.uniroma1.it/Graphs.html), by Brendan McKay and Adolfo
+Piperno:
+
+  * `ag.s6.gz` - Affine geometry graphs
+  * `cfi.s6.gz` - Cai, Fuerer and Immerman graphs
+  * `cmz.s6.gz` - Miyazaki graphs
+  * `grid.s6.gz` - Grid graphs
+  * `grid-sw.s6.gz` - Grid graphs with switched edges
+  * `had.g6.gz` - Hadamard matrix graphs
+  * `had-sw.g6.gz` - Hadamard matrix graphs with switched edges
+  * `k.g6.gz` - Complete graphs
+  * `latin.g6.gz` - Latin square graphs
+  * `latin-sw.g6.gz` - Latin square graphs with switched edges
+  * `lattice.g6.gz` - Lattice graphs
+  * `mz.s6.gz` - Miyazaki graphs
+  * `mz-aug.s6.gz` - Augmented Miyazaki graphs
+  * `mz-aug2.s6.gz` - Augmented Miyazaki graphs 2
+  * `paley.g6.gz` - Paley graphs
+  * `pg.s6.gz` - Desarguesian projective plane graphs
+  * `rnd-3-reg.s6.gz` - Random cubic graphs
+  * `sts.g6.gz` - Steiner triple system graphs
+  * `sts-sw.g6.gz` - Steiner triple system graphs with switched edges
+  * `triang.g6.gz` - Triangular graphs
+
+There are also some additional files containing graphs coming from finite geometry:
+
+  * `fining.p.gz` - contains some graphs comining from finite geometries:
+    (1): vertices are the generators of the hermitian polar space H(5,4), two vertices are adjacent iff they are skew
+    (2): vertices are the generators of the hermitian quadrangle H(4,4), two vertices are adjacent iff they are skew
+    (3): vertices areh the points and lines of the classical generalized quadrangle Q(4,8), two vertics are adjacent iff
+    they are incident (and no loops!). This is a bipartite graph with diameter 4 and undirected girth 8
+    (4): the bipartite graph (see (3)) of an elation generalized quadrangle. This one was constructed as a coset geometry. 
+    (5): the bipartite graph of the split Cayley hexagon of order 4, diameter is 6 and girth is 12.
+    (6): the bipartite graph of the Ree-Tits generalized octagon! This one has diameter 8 and girth 16!
+  
+  * `polar_graphs.p.gz` A polar graph is by definition the point graph of a
+     finite classical polar space. Note that such a geometry is a partial linear
+     space, so not every pair of points is a pair of collinear points. Two
+     points are adjacent iff they differe and they are collinear. The diamter of
+     these graphs is 2, their undirected girth 3, the latter since these spaces
+     contain lines.  Reading in this file requires around 4 Gb.
+
+  * `dual_polar_graphs.p.gz` We consider again finite classical polar
+     spaces. Such geometries contain points, lines, etc., up to maximal
+     subspaces, which all have the same projective dimension. The vertices of a
+     dual polar graph are these maximal subspaces, of dimension d say, and they
+     are adjacent iff they differ and meet in a d-1 dimensional projective
+     subspace. Reading in this file requres around 5Gb.
+     
+  * `generators_graphs.p.gz` (parts 1, 2 and 3). We consider again finite
+      classical polar spaces. The vertices are the maximal subspaces and they
+      are adjacent iff they differ and are skew. Reading part 2 requires almost
+      6Gb, reading part 3 requires again 6Gb. Reading part 1 requires much less
+      (around 1.5Gb).
+      
+  * `incidence_graphs.p.gz` a generalized polygon of gonality n is a point line
+      geometry, such that if one considers the incidence graph, i.e. the
+      vertices are the points and the lines, adjacency is incidence (withouth
+      loops), then it has diameter n and girth 2n. All graphs in this repository
+      are incidence graphs of generalized polygons. Note that by a famous
+      theorem, thick GPs (i.e. at least three points on a line and dually, at
+      least three lines on a point), have gonality 3,4,6 or 8. The repository
+      contains the incidence graph of the smallest generalized octogon, some
+      generalized hexagons, and a lot of generalized quadrangles, and some
+      projective planes.  To read it completely, around 1.5Gb is requiered.
+    
+
+which were added by Jan De Beule.

acyclic.ds6.gz

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