Resolving sets and resolving several objects in the finite king grid

An l-resolving set of a graph G is a set of vertices that has a unique array of distances to all vertex sets of G with up to l elements. The smallest cardinality of such a set is called the l-set-metric dimension of G. In this thesis, we consider mainly the l-set-metric dimension of the finite king grid. In the first section, we will introduce the problem and its background. We will also give some examples of related topics. In the second and third sections, we will present the needed definitions and notations regarding the l-resolving sets and the king grid. We will also present examples and some previous results. In the fourth and fifth sections, we will present our new results concerning the king grid. We will prove exactly what the l-set-metric dimension is for any finite king grid and value of l