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CayleyGraph

CayleyGraph[group]
returns a Cayley graph representation of group.
  • 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 .
  • Generators are represented by default using different colors, with increasing Hue values for the elements listed by GroupGenerators.
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:
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:
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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:
This is only a useful representation for small groups. For groups with a few hundred elements, the graph is generally already too complex:
A point:
A line:
A square:
A cube:
A 4D cube:
A 5D cube:
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