CayleyGraph

CayleyGraph[group]
returns a Cayley graph representation of group.

MORE INFORMATION

CayleyGraph[group] returns a graph object with head Graph.

A Cayley graph is both a description of a group and of the generators used to describe that group. The generators are those returned by the function GroupGenerators.

Group elements are represented as vertices, and generators are represented as directed edges. An edge from a group element to an element means that the product of with the generator of the edge gives .

Vertices are numbered as ordered by GroupElements and GroupElementPosition. The identity element is always numbered 1.

Generators are represented by default using different colors, with increasing Hue values for the elements listed by GroupGenerators.

EXAMPLES

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Basic Examples (1)

This is the Cayley graph connecting the 24 elements of a permutation group defined by two generators, the first represented in red and the second in blue:

In[1]:=

Out[1]=

Scope (3)

Cayley graph of the symmetric group of degree four defined by three transpositions:

Cayley graph of the symmetric group of degree four with the default generating set:

The identity permutation is removed from the list of generators:

Possible Issues (1)

This is only a useful representation for small groups. For groups with a few hundred elements, the graph is generally already too complex:

Neat Examples (1)

A point:

A line:

A square:

A cube:

A 4D cube:

A 5D cube: