Minimal doubly resolving sets and the strong metric dimension of hamming graphs

Abstract

We consider the problem of determining the cardinality ψ (H 2,k) of minimal doubly resolving sets of Hamming graphs H 2,k.We prove that for k ≥ 6 every minimal resolving set of H 2,k is also a doubly resolving set, and, consequently, ψ (H 2,k) is equal to the metric dimension of H 2,k, which is known from the literature. Moreover, we find an explicit expression for the strong metric dimension of all Hamming graphs H n,k.