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An identifying code of a (di)graph is a dominating set with the property that any two distinct vertices have distinct (in)neighbourhoods within the identifying code. Identifying codes have found many applications, such as for fault diagnosis in multiprocessor networks or the placement of emergency sensors in facilities, and have been widely studied since the introduction of the concept by Karpovsky et al. in 1998. In this talk, we present some recent results and open problems on extremal cardinalities of identifying codes.
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