Finding Open Locating Dominating Sets on Infinite and Finite Graphs

An Open Locating Dominating set is a subset of vertices of a graph such that (i) every vertex in the graph has at least one neighbor in the Open Locating Dominating set and (ii) no two vertices in the graph have the same set of neighbors in the Open Locating Dominating set. Such a set can provide insight into the structure of the graph as well as give network control or increase network robustness. We give an Integer Linear Program which finds Open Locating Dominating sets on finite graphs. Finally, we prove that the Open Locating Dominating density of the Infinite Triangular Grid is 4/13