It is well-known that the Paley graph $P(q)$ is a strongly regular graph with parameters 
$(4t+1,2t,t-1,t)$. Suppose that $v$ is a vertex in the Paley graph  $P(q)$. Suppoe that $C$ is the set of all neighbours of $v$ and $D$ be the complement of $C$. 
If one applies Godsil-Mckay switching, then under what conditions
 the new graph is non-isomorphic to the Paley graph $P(q)$?