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nauty-vcolg - Man Page

colour the vertices of graphs in all distinct ways


vcolg [-q] [-u|-T|-o] [-e#|-e#:#] [-m#] [-c#,..,#] [-f#] [infile [outfile]]


Read graphs or digraphs and colour their vertices in all possible ways with colours 0,1,2,... . Isomorphic graphs derived from the same input are suppressed. If the input graphs are non-isomorphic then the output graphs are also.

-e# | -e#:#

specify a value or range of the total value of the colours

-m# number of available colours (default 2 if -c not given)


specify the maximum number of vertices of each colour

The total must at least equal the number of vertices in the input.


minimum vertex degree for each colour (out-degree for digraphs)


maximum vertex degree for each colour (out-degree for digraphs)

-d and -D can have fewer colours than -m/-c but not more

-f# Use the group that fixes the first # vertices setwise


Use a simple text output format (nv ne {col} {v1 v2})


Use sparse6 (undirected) or digraph6 (directed) for output,

provided m=2 and the inputs have no loops.


no output, just count them


suppress auxiliary information


April 2024 nauty 2.8.8 Nauty Manual