Resolvability of some convex polytopes

Abstract

Let G = (V, E) be a simple connected graph, w V be a vertex and e = uv E be an edge. Then the distance between the vertex w and edge e is given by d(e, w)-min{d(w,u)} d{w,v)}. A vertex w distinguishes two edges tu E if d(w1,e\) ≠ d(w,e2). If every two edges of G are distinguished by some vertices of S, then it is known as edge resolving set. An edge resolving set with minimum number of elements is the basis for G and its cardinality is known as edge metric dimension, denoted by edim(G). In this paper, we study the edge metric dimension of some wheel related convex polytopes denoted by B2n. ®2n and Qn. We proved that these families have unbounded edge metric dimension. Moreover, these families of polytopes admit the relation edim(G) ≥ dim(G) between their metric dimension and edge metric dimension. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.