Journal of Prime Research in Mathematics

# Graphs with same diameter and metric dimension

Imrana Kousar
Department of Mathematics, National University of Computer and Emerging Sciences(Fast), Lahore, Pakistan.
Ioan Tomescu
Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei, 010014 Bucharest, Romania.
$$^{1}$$Corresponding Author: imrana.kousar@hotmail.com
The cardinality of a metric basis of a connected graph $$G$$ is called its metric dimension, denoted by $$dim(G)$$ and the maximum value of distance between vertices of $$G$$ is called its diameter. In this paper, the graphs $$G$$ with diameter 2 are characterized when $$dim(G) = 2.$$