On metric dimension of some planar graphs with 2n odd sided faces

Abstract

Let [Formula: see text] be a connected graph of size [Formula: see text]. If [Formula: see text] is an ordered subset of distinct vertices in [Formula: see text] then the subset [Formula: see text] is said to be a resolving set for [Formula: see text], if all of the vertices in the graph can be uniquely defined by the vector of distances to the vertices in [Formula: see text]. A resolving set [Formula: see text] with minimum possible vertices is said to be a metric basis for [Formula: see text]. The cardinality of the metric basis is called the metric dimension of the graph [Formula: see text]. In this paper, we demonstrate that the metric dimension for some families of related planar graphs is three.