The nonlocal metric dimension of a connected graph G, written as dimn(G), is the smallest possible size of a set of vertices such that allows every two non-neighbor vertices to be distinguished by the distance of a vertex from that set. In this paper, we look at some unsolved issues concerning the nonlocal metric dimension of the corona product of two graphs. In particular, we demonstrate that dimn(T Km) = (T ), where T is a tree with (T ) leaves. In addition, for a connected bipartite graph G with partite sets A and B, we show that dim(G) + min{|A|, |B|} is a sharp upper bound for dimn(G Km). We also investigate the nonlocal metric dimension of the join graph G + K1 for certain graphs G, including the fan graph and a family of trees. Furthermore, a model based on integer linear programming is proposed for determining the nonlocal metric dimension. Finally, a real-world application of the nonlocal metric dimension is presented.

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