Open neighborhood locating-domination for infinite cylinders

Abstract

For a graph G that models a facility or a multi-processor network, detection devices can be placed at the vertices so as to identify the location of an intruder such as a thief or saboteur or a faulty processor. Open neighborhood locating-dominating sets are of interest when the intruder/fault at a vertex precludes its detection by a device at that location. For example, a processor might be able to determine whether another processor directly connected to it is faulty, but it cannot be assumed to detect its own fault. In this paper we illustrate these concepts using cylindrical graphs as examples of multi-processor networks.