Let G be a graph. If  then a  geodesic of G is the shortest path between u and v. The closed interval  consists of all vertices lying in some  geodesic of G. For  the set  is the union of all sets  for  A set S is a geodetic set of G if  The cardinality of a minimum geodetic set of G is the geodetic number of G, denoted by  In this paper, we study the split geodetic number of a graph.  is a split geodetic set in G if S is a geodetic set and  is disconnected, split geodetic number  of G is the minimum cardinality of a split geodetic set of G. We investigate the relationship between split geodetic number and geodetic number. We also obtain the split geodetic number in the Cartesian product of graphs.

Cartesian product, distance, edge covering number, split geodetic number, vertex covering number.