Let G=(V,E) be a simple graph. Any partition of V(G) to k independent subsets is called a k-coloring of G. If Π={S1,S2,⋯,Sk} is a minimum such partition, then k is a chromatic number of G, denoted by χ(G)=k. A k-coloring Π={S1,S2,⋯,Sk} is said to be a (metric-)locating coloring, (an ML-coloring), if for every pair of distinct vertices u,v, with same color, there exists a color class Sj such that d(u,Sj)≠d(v,Sj). Minimum k for ML-coloring of a graph G, is called (metric-)locating chromatic number χL(G) of G. A k-neighbor locating coloring of G is a partition of V(G) to Π={S1,S2,⋯,Sk} such that for two vertices u,v∈Si, there is a color class Sj for which, one of them has a neighbor in Sj and the other not. The minimum k with this property, is said to be neighbor-locating chromatic number of G, denoted by χNL(G) of G. We initiate to continue the study of neighbor locating coloring of graphs which has been already introduced by other authors. In [1] the authors posed three conjectures and we study these conjectures. We show that, for each pair h,k of integers with 3≤h≤k, there exists a connected graph G such that χL(G)=h and χNL(G)=k, which proves the first conjecture. If G and H are connected graphs, then χNL(G[H])≤χNL(G□H), that disproves the second conjecture. Finally, we investigate for a family of graphs G, χNL(μ(G))=χNL(G)+1, where μ(G) is the Mycielski graph of G, that proves the third conjecture for some families of graphs.