@article{Tomescu2011MetricDA,
title={Metric Dimension and R-Sets of Connected Graphs},
author={Ioan Tomescu and Muhammad Imran},
journal={Graphs and Combinatorics},
year={2011},
volume={27},
pages={585-591}
}

The R-set relative to a pair of distinct vertices of a connected graph G is the set of vertices whose distances to these vertices are distinct. This paper deduces some properties of R-sets of connected graphs. It is shown that for a connected graph G of order n and diameter 2 the number of R-sets equal to V (G) is bounded above by n2/4 . It is conjectured that this bound holds for every connected graph of order n. A lower bound for the metric dimension dim(G) of G is proposed in terms of a… CONTINUE READING