One-factor Resolvability of Grid derived Networks

Given a graph \( G = (V, E) \), a set \( W \subseteq V \) is said to be a resolving set if for each pair of distinct vertices \( u, v \in V \), there is a vertex \( x \) in \( W \) such that \( d(u, x) \neq d(v, x) \). The resolving number of \( G \) is the minimum cardinality of all resolving sets. In this paper, a condition is imposed on resolving sets and a conditional resolving parameter is studied for grid-based networks.