Cayley's theorem
The group formula_1 acts on itself by left multiplication (see Cayley's theorem). This may be viewed as the action of formula_1 on its Cayley graph. Explicitly, an element formula_65 maps a vertex formula_66 to the vertex formula_67 The set of edges of the Cayley graph and their color is preserved by this action: the edge formula_68 is mapped to the edge formula_69, both having color formula_11. The left multiplication action of a group on itself is simply transitive, in particular, Cayley graphs are vertex-transitive. The following is a kind of converse to this: