Computing vertex resolvability of some regular planar graphs

Abstract

Let [Formula: see text] be a connected graph of order n. An ordered subset [Formula: see text] of vertices in [Formula: see text] is said to be a resolving set for [Formula: see text], if all the vertices of [Formula: see text] are uniquely determined by the vector of distances to the vertices in [Formula: see text]. The metric dimension of [Formula: see text] is the minimum cardinality of a resolving set [Formula: see text] and that resolving set is the metric basis for [Formula: see text]. In this paper, we show that the metric dimension is three for a family of a three-regular convex polytope.