A set of generators
is a set of group elements such that possibly repeated application of the generators
on themselves and each other is capable of producing all the elements in the group.
Cyclic groups can be generated as powers
of a single generator. Two elements of a dihedral group
that do not have the same sign of ordering are generators for the entire group.

The Cayley graph of a group and a subset of elements (excluding the identity
element) is connected iff the subset generates the group.