Let G be a group and S be a symmetric subset of G (i.e., S−1 = S). The Cayley graph Cay(G, S) is the graph whose vertices are the elements of G and two distinct vertices g and h are adjacent if and only if g −1h ∈ S. Now, let H be a subgroup of G and S be a subset of G where S ∩ H is a symmetric subset of H. The group-subgroup pair graph, or briefly pair graph, which is denoted by Cay(G, H, S), is the undirected graph with vertices G and simple edges given by (h, hs) for all h ∈ H, s ∈ S. If we set H = G, then the pair graph Cay(G, H, S) is isomorphic to the Cayley graph Cay(G, S) which means that the pair graph is a generalization of Cayley graphs. In this paper, we study the local metric dimension of Cay(G, H, S). Also, we investigate the metric dimension, local metric dimension and edge metric dimension of Cay(Zn, H, S)

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