Abstract
A locating-dominating set is a subset of vertices in a graph, which is used to model a detection system for a facility or network. A detector placed at each vertex v in the subset is assumed to detect an “intruder” at v as well as in its neighborhood. Any system that is modeled by a locating-dominating set can precisely determine the exact location of the intruder from the information provided by these detectors. We explore two fault-tolerant variants of locating-dominating sets, namely redundant locating-dominating (RED:LD) and error-correcting locating-dominating (ERR:LD) sets. The problems of determining the minimum cardinality of RED:LD and ERR:LD sets in arbitrary graphs are known to be NP-complete. In this paper we determine the lower and upper bounds on values of the minimum densities of RED:LD and ERR:LD sets in cubic graphs, and present cubic graphs that achieve the extremal values on these parameters.
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