Minimal resolving sets for the hypercube

For a given undirected graph G, an ordered subset S = {s1, s2, . . . , sk} ⊆ V of vertices is a resolving set for the graph if the vertices of the graph are distinguishable by their vector of distances to the vertices in S. While a superset of any resolving set is always a resolving set, a proper subset of a resolving set is not necessarily a resolving set, and we are interested in determining resolving sets that are minimal or that are minimum (of minimal cardinality). Let Q denote the n-dimensional hypercube with vertex set {0, 1}. In Erdös and Renyi [5] it was shown that a particular set of n vertices forms a resolving set for the hypercube. The main purpose of this note is to prove that a proper subset of that set of size n − 1 is also a resolving set for the hypercube for all n ≥ 5 and that this proper subset is a minimal resolving set.