Encoding Structures into Graphs Using Cayley Graphs

type of group

Symmetric

Alternating

Cyclic

Dihedral

order

2

3

4

5

A set of elements of a group

G

is said to generate (or to be the generators of)

G

if the (possibly repeated) application of the generators on themselves and each other is capable of producing all the elements in the group. Given a set of generators (which are obtained by using the built-in Mathematica 8 function GroupGenerators) of

G

, the Cayley graph associated with

G

is defined as the directed connected graph having one vertex associated with each group element and directed edges

ab

whenever

a

-1

b

is a generator. In this Demonstration we construct the Cayley graphs of several types of groups using the CayleyGraph function.