# Cayley graph of a group

## Definition

Let be a group and be a generating set for . The **Cayley graph** of with respect to is defined as follows:

- The vertex set of the graph is .
- Given two distinct vertices , there is an edge joining to if and only if is in .

We typically consider the Cayley graph for a finitely generated group and a finite generating set of the group. Further, we can assume without loss of generality that is a symmetric subset of -- the inverse of any element of is also in .