On the Metric Dimension of Rotationally-Symmetric Graphs

Abstract

A family $\mathcal{G}$ of connected graphs is a family with constant metric dimension if $\dim (G)$ is finite and does not depend upon the choice of $G$ in $\mathcal{G}$. The metric dimension of some classes of plane graphs has been determined in $[2],[3],[4],[9],[10],[14],[22]$. In this paper, we extend this study by considering some classes of plane graphs which are rotationally-symmetric. It is natural to ask for the characterization of classes of rotationally-symmetric plane graphs with constant metric dimension.