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A detection system, modeled in a graph, is composed of "detectors" positionedat a subset of vertices in order to uniquely locate an ``intruder" at anyvertex. \emph{Identifying codes} use detectors that can sense the presence orabsence of an intruder within distance one. We introduce a fault-tolerantidentifying code called a \emph{redundant identifying code}, which allows atmost one detector to go offline or be removed without disrupting the detectionsystem. In real-world applications, this would be a necessary feature, as itwould allow for maintenance on individual components without disabling theentire system. Specifically, we prove that the problem of determining thelowest cardinality of an identifying code for an arbitrary graph isNP-complete, we determine the bounds on the lowest cardinality for specialclasses of graphs, including trees, cylinders, and cubic graphs.

Fault-tolerant Identifying Codes in Special Classes of Graphs