The concept of resolving sets and metric basis are the derived to handle these situations. One is interested to assign a unique address to each node to easily communicate and identify the failure of any device or node in this network of computers. In graph and network theory, computer networks are treated as graphs with vertices as nodes and edges as communication media. Almost twenty years later, Slater pointed out a potential application of detection problem in graph theory, which brought these ideas again in the spotlight but now in the context of discrete cases like graphs and networks. But it did not attract much attention at that probably because of linear continuum nature of R n. Resolving set and metric basis appeared on the scene way back in 1953 for an arbitrary metric space by Blumenthal.
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