# nauty-countg - Man Page

count graphs according to a variety of properties

## Synopsis

**[pickg|countg]** [*-fp#:#q -V -X*] [*--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 (but not

**-p**)- -X
Reverse selection (but

**-p**still observed)- -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.

- -1
Write output as lines of numbers separated by spaces, with 0/1 for boolean and both endpoints of ranges given separately even if they are the same, and the count at the end of the line. Also, no total is written.

- -2
The same as

**-1**but counts are not written.- -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

**-ee**# number of non-edges (including loops for digraphs)

- -L#
number of loops

**-C**strongly connected

**-LL**# number of 2-cycles **-cc**# number of components

- -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 (in-)degree

**-S**# vertices of max (in-)degree- -r
regular

**-b**bipartite- -z#
radius

**-Z**# diameter- -g#
girth (0=acyclic)

**-Y**# total number of cycles- -h#
maximum independent set

**-k**# maximum clique- -T#
number of triangles

**-K**# number of maximal cliques- -TT# number independent 3-sets -P#
number of 5-cycles

- -B#
smallest possible first side of a bipartition (0 if nonbipartite)

- -H#
number of induced cycles

**-W**# number of 4-cycles- -E
Eulerian (all degrees are even, connectivity not required)

- -a#
group size

**-o**# orbits**-F**# fixed points**-t**vertex-transitive- -c#
connectivity (2 means 2 or more).

**-kk**# #-tree, otherwise 0. The complete graph K_n is tabulated as

an n-tree, but matches either n-1 or n,

- -i#
min common nbrs of adjacent vertices;

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

**-jj**# maximum- -x#
number of sources

**-xx**# number of sinks

**-WW**# number of diamonds

- -N#
chromatic number (limited to WORDSIZE colours)

**-NN**# chromatic index (limited to max degree WORDSIZE-1)

**-AA**# class (chromatic index - maximum degree + 1)

- -G#
connectivity

**-GG**# edge connectivitySort 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. A comma can be used as a separator.The sort key ':' has a special purpose: the values of sort keys following ':' are given as ranges rather than creating a separate line for each value. For example

**--e**:zZ will give the ranges of radius and diameter that occur for each number of edges. The output format matches the input, except that sparse6 is used to output an incremental graph whose predecessor is not output.Some sort keys have boolean variants with parameters:

- --N#
#-colourable (i.e. chromatic number <= #)

- --A#
#-edge colourable

- --G#
#-connected (i.e. connectivity >= #)

**--GG**# #-edge connected