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NAUTY-PICKG

NAME

nauty-pickg − select 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.

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