Minimum weight resolving sets of grid graphs

Abstract

For a simple graph [Formula: see text] and for a pair of vertices [Formula: see text], we say that a vertex [Formula: see text] resolves [Formula: see text] and [Formula: see text] if the shortest path from [Formula: see text] to [Formula: see text] is of a different length than the shortest path from [Formula: see text] to [Formula: see text]. A set of vertices [Formula: see text] is a resolving set if for every pair of vertices [Formula: see text] and [Formula: see text] in [Formula: see text], there exists a vertex [Formula: see text] that resolves [Formula: see text] and [Formula: see text]. The minimum weight resolving set problem is to find a resolving set [Formula: see text] for a wei..