Properties
In Chartrand, Eroh & Oellermann (2000), it is proved that:
- The metric dimension of a graph G is 1 if and only if G is a path.
- The metric dimension of an n-vertex graph is n − 1 if and only if it is a complete graph.
- The metric dimension of an n-vertex graph is n − 2 if and only if the graph is a complete bipartite graph Ks, t, a split graph, or .
Khuller, Raghavachari & Rosenfeld (1996) prove the inequality for any n-vertex graph with diameter D and metric dimension β.
Read more about this topic: Metric Dimension (graph Theory)
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