Math Overflow hi,

I would like to show that Paley graph are rank 3-graphs (i.e Vertex-Transitive, Edge-Transitive and Non-Edge-Transitive).

Showing that they are Vertex transitive is easy - every x |-> x+k is an automorphism in GF(q) and so, for example, the automorphism x|-> x+1 shows that they are vertex transitive.

I also know how to show that they are self-complimentary and thus if I can show on of edge-transitivity/non-edge transitivity I get the other.

Can anyone help with how to show that they are indeed edge-transitive (or non-edge-transitive)

Thanks!