A set S of vertices of a graph G is a geodetic set if every vertex of G lies in a shortest path
between some pair of vertices of S. The Minimum Geodetic Set (MGS) problem is to find a …

We study the complexity of finding the\emph {geodetic number} on subclasses of planar
graphs and chordal graphs. A set $ S $ of vertices of a graph $ G $ is a\emph {geodetic set} …

The strong geodetic problem is a recent variation of the classical geodetic problem. For a
graph G, its strong geodetic number sg (G) sg (G) is the cardinality of a smallest vertex …

Partially answering a question posed by Araujo, Morel, Sampaio, Soares, and Weber, we
show that computing the geodetic hull number of a given P 9-free graph is NP-hard …

Given a graph G and a pair of vertices u, v the interval IG [u, v] is the set of all vertices that
are in some shortest path between u and v. Given a subset X of vertices of G, the interval IG …

The strong geodetic problem is a recent variation of the geodetic problem. For a graph G, its
strong geodetic number sg (G) is the cardinality of a smallest vertex subset S, such that each …

A recent variation of the classical geodetic problem, the strong geodetic problem, is defined
as follows. If G is a graph, then sg (G) sg (G) is the cardinality of a smallest vertex subset S …

A vertex set S of a graph G is a strong geodetic set if it is possible to choose exactly one
shortest path for each pair of vertices in S, and cover all the remaining vertices of the graph …

In this paper, we study the computational complexity of finding the geodetic number of
graphs. A set of vertices S of a graph G is a geodetic set if any vertex of G lies in some …

Let G=(V(G),E(G)) be a graph and S be a subset of vertices of G. Let us denote by γu,va
geodesic between u and v. Let Γ(S)={γv_i,v_j|v_i,v_j∈S be a set of exactly |S|(|S|−1)//2 …