An O(mn^2) algorithm for computing the strong geodetic number in outerplanar graphs

Mauro Mezzini
2020 Discussiones Mathematicae Graph Theory  
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 the
more » ... ong geodetic number of an outerplanar graph can be computed in polynomial time.
doi:10.7151/dmgt.2311 fatcat:2po5ulzmurdbxmehwwdagtp44i