On hendecagonal circular ladder and its metric dimension

Let $ \Gamma =(V,E) $ Γ=(V,E)be a connected graph of order n. Two vertices pand qin Vare said to resolve by a vertex $ x \in V $ x∈Vif $ d(p,x)\neq d(q,x) $ d(p,x)≠d(q,x). An ordered subset $ F=\{k_{1},k_{2},k_{3},\dots,k_{l}\} $ F={k1,k2,k3,…,kl}of vertices in Γ is said to be resolving set if for every pair p, qof distinct vertices in V, we have $ \zeta (p|F)\neq \zeta (q|F) $ ζ(p|F)≠ζ(q|F), where $ \zeta (a|F)=(d(a,k_{1}),d(a,k_{2}),d(a,k_{3}),\dots,d(a,k_{l})) $ ζ(a|F)=(d(a,k1),d(a,k2),d(a,k3),…,d(a,kl))is the l-code/metric coordinate representation of the vertex awith respect to the set F. The resolving set for Γ with minimum cardinality is known as metric basis for the graph Γ and the cardinality of metric basis is called as metric dimension of Γ. In this work, we demonstrate that for two families of convex polytopes which are closely linked, the metric dimension is constant.