(untitled) (European Journal of Pure and Applied Mathematics, 2023)
Let G be an undirected graph with vertex-set V(G) and edge-set E(G), respectively. A set SV(G) is a 2-locating set of G if |[(N_G(x)N_G(y))S] [(N_G(y)N_G(x))S]|≥ 2, for all x,yV(G)S with x eq y, and for all vS and wV(G)S, (N_G(v)N_G(w))S eq or (N_G(w)N_G[v]) S eq . In this paper, we investigate the concept and study 2-locating sets in graphs resulting from some binary operations. Specifically, we characterize the 2-locating sets in the join, corona, edge corona and lexicographic product of graphs, and determine bounds or exact values of the 2-locating number of each of these graphs.