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Let G = (V (G), E(G)) be a graph and S be a subset of vertices of G. Let us denote by γ [u, v] a geodesic between u and v. Let be the set of all vertices contained in all the geodesics in Γ(S). If V (Γ(S)) = V (G) for some Γ(S), then we say that S is a strong geodetic set of G. The cardinality of a minimum strong geodetic set of a graph is the strong geodetic number of G. It is known that it is NP-hard to determine the strong geodetic number of a general graph. In this paper we show that thedoi:10.7151/dmgt.2311 fatcat:2po5ulzmurdbxmehwwdagtp44i