Computation of Metric Dimension of Certain Subdivided Convex Polytopes

Abstract

The distance dz1,z2 from vertex z1∈VG to z2∈VG is minimum length of z1,z2-path in a given connected graph G having E(G) and V(G) edges and vertices’/nodes’ sets, respectively. Suppose Z=z1,z2,z3,…,zm⊆VG is an order set and c∈VG, and the code of c with reference to Z is the m-tuple {d(c, z1), d(c, z2), d(c, z13), …, d(c, zk)}. Then, Z is named as the locating set or resolving set if each node of G has unique code. A locating set of least cardinality is described as a basis set for the graph G, and its cardinal number is referred to as metric dimension symbolized by dimG. Metric dimension of certain subdivided convex polytopes STn has been computed, and it is concluded that just four vertices are sufficient for unique coding of all nodes belonging to this family of convex polytopes.