Metric Dimension and R-Sets of Connected Graphs

@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

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