1NAUTY-COUNTG(1)                  Nauty Manual                  NAUTY-COUNTG(1)
2
3
4

NAME

6       nauty-countg - count graphs according to a variety of properties
7

SYNOPSIS

9       [pickg|countg]  [-fp#:#q  -V  -X]  [--keys]  [-constraints  -v]  [ifile
10       [ofile]]
11

DESCRIPTION

13              countg : Count graphs according to their properties.
14
15              pickg : Select graphs according to their properties.
16
17              ifile, ofile : Input and output files.
18
19              '-' and missing names imply stdin and stdout.
20
21              Miscellaneous switches:
22
23       -p# -p#:#
24              Specify range of input lines (first is 1) May fail if  input  is
25              incremental.
26
27       -f     With  -p,  assume  input lines of fixed length (only used with a
28              file in graph6/digraph6 format)
29
30       -v     Negate all constraints (but not -p)
31
32       -X     Reverse selection (but -p still observed)
33
34       -V     List properties of every input matching constraints.
35
36       -l     Put a blank line whenever the first parameter changes, if  there
37              are at least two parameters.
38
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.
43
44       -2     The same as -1 but counts are not written.
45
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
58
59       -L#    number of loops              -C   strongly connected
60
61       -d#    minimum (out-)degree         -D#  maximum (out-)degree
62
63       -m#    vertices of min (out-)degree -M#  vertices of max (out-)degree
64
65       -u#    minimum (in-)degree          -U#  maximum (in-)degree
66
67       -s#    vertices of min (out-)degree -S#  vertices of max (out-)degree
68
69       -r     regular                      -b   bipartite
70
71       -z#    radius                       -Z#  diameter
72
73       -g#    girth (0=acyclic)            -Y#  total number of cycles
74
75       -h#    maximum independent set      -k#  maximum clique
76
77       -T#    number of triangles          -K#  number of maximal cliques
78
79       -B#    smallest  possible  first  side of a bipartition (0 if nonbipar‐
80              tite)
81
82       -H#    number of induced cycles
83
84       -E     Eulerian (all degrees are even, connectivity not required)
85
86       -a#    group size  -o# orbits  -F# fixed points  -t vertex-transitive
87
88       -c#    connectivity (only implemented for 0,1,2).
89
90       -i#    min common nbrs of adjacent vertices;     -I# maximum
91
92       -j#    min common nbrs of non-adjacent vertices; -J# maximum
93
94              Sort keys:
95
96       Counts are made for all graphs passing the constraints.
97              Counts
98
99              are given separately for each combination  of  values  occurring
100              for  the  properties  listed as sort keys.  A sort key is intro‐
101              duced by '--' and uses one of the letters known as  constraints.
102              These  can  be  combined:  --n --e  --r  is the same as --ne --r
103              and --ner.  The order of sort keys is significant.
104
105              The sort key ':' has a special purpose: the values of sort  keys
106              following  ':'  are given as ranges rather than creating a sepa‐
107              rate line for each value.  For  example  --e:zZ  will  give  the
108              ranges  of  radius  and  diameter  that occur for each number of
109              edges.  The output format matches the input, except that sparse6
110              is  used to output an incremental graph whose predecessor is not
111              output.
112
113
114
115nauty 2.7.1                        July 2020                   NAUTY-COUNTG(1)