Locating–paired-dominating sets in square grids

A set SS of vertices of a graph GG is paired-dominating if SS induces a matching in GG and SS dominates all vertices of GG. A set S⊂V(G)S⊂V(G) is locating if for any two distinct vertices u,v∈V(G)∖Su,v∈V(G)∖S, N(u)∩S≠N(v)∩SN(u)∩S≠N(v)∩S, where N(u)N(u) and N(v)N(v) are open neighborhoods of vertices uu and vv. We give a complete characterization of locating–paired-dominating sets with minimal density in the infinite square grid Z2Z2.