Strong geodomination in graphs

Abstract. A pair \(x\), \(y\) of vertices in a nontrivial connected graph \(G\) is said to geodominate a vertex \(v\) of \(G\) if either \(v \in \{x, y\}\) 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 strong geodomination in a graph \(G\).