Subsections

• The Automorphism Group Function
• Variants of Automorphism Group

Compute the automorphism group of the graph G. Note that G may be directed or undirected. For small graphs (i.e. having less than 500 vertices) the canonically labelled graph is also returned.

AutomorphismGroup( G: parameters) : Grph -> GrpPerm, Grph

Compute the automorphism group of the graph G according to the parameters parameters. There are five principal parameters: Canonical, Stabilizer, Invariant, TCLevel and Print. Some of these parameters have associated parameters.

    Canonical: BoolElt                  Default: false

If the parameter Canonical is set true, then the canonically labelled graph will be returned. If the graph has fewer than 500 vertices then the default value for this parameter is true, while if the graph has 500 or more vertices, the default value is false.

    Stabilizer: [ { Vert } ]            Default: Null

If the parameter Stabilizer is assigned a partition P of the vertex-set of G as its value, then the subgroup of the automorphism group of G that preserves the partition P will be computed. There is one optional associated Boolean parameter (Ordering) with default value true.

    Invariant: MonStgElt                Default: Null

Use the named invariant to assist the auto group computation. The invariant is specified by a string which is the name of a C-function computing an invariant, as on page 14 of the nauty manual.

There are three optional associated parameters:

    Minlevel: RngIntElt                 Default: 0

    Maxlevel: RngIntElt                 Default: 0

    Arg: RngIntElt                      Default: 0

An expression, depending upon the type of invariant.

    TCLevel: RngIntElt                  Default: 6

Specify the rule used to select the target cell by using the integer parameter TCLevel (see p6 of the nauty manual).

    Print: RngIntElt                    Default: 0

The integer valued parameter Print is used to control informative printing according to the following table:

Print := 0

No output (default).

Print := 1

Statistics are printed.

Print := 2

Summary upon completion of each level.

Print := 3

Print the automorphisms as they are discovered.

Given a graph G, return the canonically labelled graph isomorphic to G. The parameters parameters are identical to those for AutomorphismGroup.

Construct the automorphism group of the graph G in its action on the edges of G.

IsIsomorphic(G, H) : GrphUnd, GrphUnd -> BoolElt, Map

This function returns true if the graphs G and H are isomorphic. If G and H are isomorphic, a second value is returned, namely a mapping between the vertices of G and the vertices of H giving the isomorphism.