Weak geodomination in graphs


A pair x, y of vertices in a nontrivial connected graph G is said to geodominate a vertex v of G if either v ∈ {x, y} or v lies in an x − y geodesic of G. A set S of vertices of G is a geodominating set if every vertex of G is geodominated by some pair of vertices of S. In this paper we study weak geodomination in a graph G.