  A graph automorphism is a bijective mapping of the vertices that preserves
adjacent vertices. A vertex determining set of a graph is a set of vertices
such that the only automorphism that fixes those vertices is the identity. The
size of a smallest such set is called the determining number, denoted Det$(G)$.
The determining number is a parameter of the graph capturing its level of
symmetry. We introduce the related concept of an edge determining set and
determining index, Det$'(G)$. We prove that Det$'(G) \le \text{Det}(G) \le
2\text{Det}'(G)$ when Det$(G) \neq 1$ and show both bounds are sharp for
infinite families of graphs. Further, we investigate properties of these new
concepts, as well as provide the determining index for several families of
graphs.
