1NAUTY-COUNTG(1)                  Nauty Manual                  NAUTY-COUNTG(1)
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NAME

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

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

13              countg : Count graphs according to their properties.
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15              pickg : Select graphs according to their properties.
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17              ifile, ofile : Input and output files.
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19              '-' and missing names imply stdin and stdout.
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21              Miscellaneous switches:
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23       -p# -p#:#
24              Specify range of input lines (first is 1) May fail if  input  is
25              incremental.
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27       -f     With  -p,  assume  input lines of fixed length (only used with a
28              file in graph6/digraph6 format)
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30       -v     Negate all constraints (but not -p)
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32       -X     Reverse selection (but -p still observed)
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34       -V     List properties of every input matching constraints.
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36       -l     Put a blank line whenever the first parameter changes, if  there
37              are at least two parameters.
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39       -1     Write  output  as lines of numbers separated by spaces, with 0/1
40              for boolean and both endpoints of ranges given  separately  even
41              if  they  are  the  same,  and the count at the end of the line.
42              Also, no total is written.
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44       -2     The same as -1 but counts are not written.
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46       -q     Suppress informative output.
47
48              Constraints:
49
50              Numerical constraints (shown here with following #) can  take  a
51              single  integer value, or a range like #:#, #:, or :#.  Each can
52              also be preceded by  '~',  which  negates  it.    (For  example,
53              -~D2:4 will match any maximum degree which is _not_ 2, 3, or 4.)
54              Constraints are applied to all  input  graphs,  and  only  those
55              which match all constraints are counted or selected.
56
57       -n#    number of vertices           -e#  number of edges
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59       -ee# number of non-edges (including loops for digraphs)
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61       -L#    number of loops              -C   strongly connected
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63       -LL# number of 2-cycles           -cc# number of components
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65       -d#    minimum (out-)degree         -D#  maximum (out-)degree
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67       -m#    vertices of min (out-)degree -M#  vertices of max (out-)degree
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69       -u#    minimum (in-)degree          -U#  maximum (in-)degree
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71       -s#    vertices of min (in-)degree  -S#  vertices of max (in-)degree
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73       -r     regular                      -b   bipartite
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75       -z#    radius                       -Z#  diameter
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77       -g#    girth (0=acyclic)            -Y#  total number of cycles
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79       -h#    maximum independent set      -k#  maximum clique
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81       -T#    number of triangles          -K#  number of maximal cliques
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83       -TT# number independent 3-sets    -P#
84              number of 5-cycles
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86       -B#    smallest  possible  first  side of a bipartition (0 if nonbipar‐
87              tite)
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89       -H#    number of induced cycles     -W#  number of 4-cycles
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91       -E     Eulerian (all degrees are even, connectivity not required)
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93       -a#    group size  -o# orbits  -F# fixed points  -t vertex-transitive
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95       -c#    connectivity (2 means 2 or more).
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97       -kk# #-tree, otherwise 0. The complete graph K_n is tabulated as
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99              an n-tree, but matches either n-1 or n,
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101       -i#    min common nbrs of adjacent vertices;     -ii# maximum
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103       -j#    min common nbrs of non-adjacent vertices; -jj# maximum
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105       -x#    number of sources            -xx#  number of sinks
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107       -WW# number of diamonds
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109       -N#    chromatic number (limited to WORDSIZE colours)
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111       -NN# chromatic index (limited to max degree WORDSIZE-1)
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113       -AA# class (chromatic index - maximum degree + 1)
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115       -G#    connectivity                 -GG# edge connectivity
116
117              Sort keys:
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119       Counts are made for all graphs passing the constraints.
120              Counts
121
122              are given separately for each combination  of  values  occurring
123              for  the  properties  listed as sort keys.  A sort key is intro‐
124              duced by '--' and uses one of the letters known as  constraints.
125              These  can  be  combined:  --n --e  --r  is the same as --ne --r
126              and --ner.  The order of sort keys is significant.  A comma  can
127              be used as a separator.
128
129              The  sort key ':' has a special purpose: the values of sort keys
130              following ':' are given as ranges rather than creating  a  sepa‐
131              rate  line  for  each  value.  For  example --e:zZ will give the
132              ranges of radius and diameter that  occur  for  each  number  of
133              edges.  The output format matches the input, except that sparse6
134              is used to output an incremental graph whose predecessor is  not
135              output.
136
137              Some sort keys have boolean variants with parameters:
138
139       --N#   #-colourable (i.e. chromatic number <= #)
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141       --A#   #-edge colourable
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143       --G#   #-connected (i.e. connectivity >= #)
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145       --GG# #-edge connected
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149nauty 2.8.8                      November 2023                 NAUTY-COUNTG(1)