In a connected graph G = (V, E), the set S is a minimum split geodetic set. A subset T ⊆ S is called as the forcing subset for S if S is the unique minimum split geodetic set of G containing T. The minimum cardinality of a forcing subset of S is the forcing split geodetic number fs(S) of S. The forcing split geodetic number of a connected graph G is fs(G) = min{fs(S): S is a split geodetic set of G}. The set S is a minimum non-split geodetic set in a connected graph G = (V, E) and the subset T ⊆ S is called as forcing subset for S if S is the unique minimum non-split geodetic set of G containing T. The minimum cardinality of a forcing subset of S is the forcing non-split geodetic number fns(S) of S. The forcing non split geodetic number of a connected graph G is fns(G) = min{fns(S): S is a non − split geodetic set of G}. Here we determined forcing split and non-split geodetic number of certain classes of graphs. Further, we determine the forcing split and forcing non-split geodetic number of graphs under some binary operations such join, Cartesian product and corona of two graphs