Abstract. Let D be a digraph and let f be an invariant of D. Then D is called

  1. minimal by f, if f(D-e) differs from f(D) for every arc e of D;
  2. critical by f, if f(D-u) differs from f(D) for every vertex v of D;
  3. maximal by f, if f(D+e) differs from f(D) for every arc e of the complement of D;
We consider digraphs minimal, critical and maximal by three types of radii. Some of the classes are completely characterized, while for the others we show that they are large in terms of induced subgraphs.