Abstarct: A subset D of vertices in a graph G = (V ;E) is an open neighborhood locating-dominating set ( OLD-set ) for G if for every two vertices u, v of V (G) the sets N(u) ∩D and N(v) ∩D are non-empty and different. The open neighborhood locating-domination number OLD(G) is the minimum cardinality of an OLD-set for G. It is shown in this thesis that the problem finding the open neighborhood locating-dominating number NP-complete problems. Then, we describe minimum possible percentage of vertex OLD-sets for various infinte grid graphs. Also, we examin the results of the open neighborhood locating domination number on paths, trees and graphs and the bounds for open neighborhood locating domination number for these types of graphs.