On the orbital diameter of classical groups in standard actions

Let G be a primitive permutation group acting on a finite set X . The orbital diameter diam(X,G) diam ( X , G ) is defined to be the supremum of the diameters of the (connected) orbital graphs of G after disregarding the directions of all edges in the graphs. This invariant is studied in the case when G is an almost simple group in a standard action. A lower bound is given for diam(X,G) diam ( X , G ) , and we provide a partial classification of pairs ( X , G ) for which the orbital diameter is at most 2.