On metric dimension of hendecagonal circular ladder $H_{n}$

Abstract

Let $\zeta=(V,E)$ be a $n$th order connected graph. If the distance vectors to the vertices in an ordered subset $G$ of vertices can uniquely identify each vertex of the graph $\zeta$, then the set $G$ is known as resolving set for the graph $\zeta$. The resolving set $G$ with smallest cardinality serves as the metric dimension of graph $\zeta$ and this resolving set serves as the metric basis for $\zeta$. In this article, two families of convex polytopes that are closely linked are demonstrated and it is found that the metric dimension is three for both the families.