NAME

       nauty-countg - count graphs according to a variety of properties

SYNOPSIS

       [pickg|countg] [-fp#:#q -V] [--keys] [-constraints -v] [ifile [ofile]]

DESCRIPTION

              countg : Count graphs according to their properties.

              pickg : Select graphs according to their properties.

              ifile, ofile : Input and output files.

              '-' and missing names imply stdin and stdout.

              Miscellaneous switches:

       -p# -p#:#
              Specify range of input lines (first is 1) May fail if input is incremental.

       -f     With   -p,  assume  input  lines  of  fixed  length  (only  used  with  a  file  in
              graph6/digraph6 format)

       -v     Negate all constraints

       -V     List properties of every input matching constraints.

       -l     Put a blank line whenever the first parameter changes, if there are  at  least  two
              parameters.

       -q     Suppress informative output.

              Constraints:

              Numerical  constraints  (shown  here  with  following  #) can take a single integer
              value, or a range like #:#, #:, or :#.  Each can also be  preceded  by  '~',  which
              negates  it.   (For example, -~D2:4 will match any maximum degree which is _not_ 2,
              3, or 4.)  Constraints are applied to all input graphs, and only those which  match
              all constraints are counted or selected.

       -n#    number of vertices           -e#  number of edges

       -L#    number of loops              -C   strongly connected

       -d#    minimum (out-)degree         -D#  maximum (out-)degree

       -m#    vertices of min (out-)degree -M#  vertices of max (out-)degree

       -u#    minimum (in-)degree          -U#  maximum (in-)degree

       -s#    vertices of min (out-)degree -S#  vertices of max (out-)degree

       -r     regular                      -b   bipartite

       -z#    radius                       -Z#  diameter

       -g#    girth (0=acyclic)            -Y#  total number of cycles

       -T#    number of triangles          -K#  number of maximal cliques

       -B#    smallest side of some bipartition (0 if none)

       -H#    number of induced cycles

       -E     Eulerian (all degrees are even, connectivity not required)

       -a#    group size  -o# orbits  -F# fixed points  -t vertex-transitive

       -c#    connectivity (only implemented for 0,1,2).

       -i#    min common nbrs of adjacent vertices;     -I# maximum

       -j#    min common nbrs of non-adjacent vertices; -J# maximum

              Sort keys:

       Counts are made for all graphs passing the constraints.
              Counts

              are  given  separately  for each combination of values occurring for the properties
              listed as sort keys.  A sort key is introduced by '--' and uses one of the  letters
              known  as  constraints.   These can be combined:  --n --e  --r  is the same as --ne
              --r and --ner.  The order of sort keys is significant.

              The output format matches the input, except that  sparse6  is  used  to  output  an
              incremental graph whose predecessor is not output.