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.