On Constant Metric Dimension of Some Generalized Convex Polytopes

Abstract

Metric dimension is the extraction of the affine dimension (obtained from Euclidean space $E^d$ ) to the arbitrary metric space. A family $\mathrm{ℱ}=\left(G_n\right)$ of connected graphs with $n\ge 3$ is a family of constant metric dimension if $\dim \left(G\right)=k$ (some constant) for all graphs in the family. Family $\mathrm{ℱ}$ has bounded metric dimension if $\dim \left(G_n\right)\le M$ , for all graphs in $\mathrm{ℱ}$ . Metric dimension is used to locate the position in the Global Positioning System (GPS), optimization, network theory, and image processing. It is also used for the location of hospitals and other places in big cities to trace these places. In this paper, we analyzed the features and metric dimension of generalized convex polytopes and showed that this family belongs to the family of bounded metric dimension.