Sharp bound on the truncated metric dimension of trees

A k-truncated resolving set of a graph is a subset S⊆V of its vertex set such that the vector (d_k(s,v))_s∈S is distinct for each vertex v∈V where d_k(x,y)=min⁡{d(x,y),k+1} is the graph distance truncated at k+1. We think of elements of a k-truncated resolving set as sensors that can measure up to distance k. The...