Let G be a group, and let S⊆G be a set of group elements such that the identity element I not element S. The Cayley graph associated with (G, S) is then defined as the directed graph having one vertex associated with each group element and directed edges (g, h) whenever g h^(-1) element S. The Cayley graph may depend on the choice of a generating set, and is connected iff S generates G (i.e., the set S are group generators of G).
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