Computational complexity of Seidel's switching

Seidel's switching of a vertex in a graph is an operation that results in making this vertex adjacent to exactly those vertices that previously have not been its neighbors. Two graphs are called switching equivalent if one can be turned into (an isomorphic copy of) the other one.

This operation has applications in geometrical configurations called equiangular line systems, it can be described - in a very elegant way - by linear algebraic terms and it has unexpected applications in hypergraphs called the $P_4$-structures of graphs. Several authors have considered the meta-question "Given a graph, how difficult is it to decide if it can be switched to a graph having a certain property $P$?"

I will survey these results and concentrate on the most recent one, the question of switching a given graph to a graph with minimum possible number of edges.

The last mentioned result is a joint work with Eva Jelinkova nad Vit Jelinek.