Let  be a graph. A set  is a strong k-geodetic set if each vertex  lies on a fixed k-geodesic between some pair of vertices of S. The minimum cardinality of a strong k-geodetic set is the strong k-geodetic number of G and is denoted by  In this paper we have derived some results on the strong k-geodetic number. Also we prove that the strong k-geodetic problem is NP-complete for general graphs, bipartite graphs, chordal graphs and chordal bipartite graphs.

geodetic set, strong geodetic set, k-geodetic set, strong k-geodetic set.