If all the sets I(v) are nonempty and pairwise different, then C is called an identifying code. This concept was introduced in in connection with studying multiprocessor architectures. Such an architecture can be viewed as a graph, where each vertex represents a processor, and each edge represents a dedicated link between two processors. Assume that at most one of the processors is malfunctioning. Each of the chosen codewords c tests the sets B1(c) and reports YES if it detects a problem and NO otherwise. The fact that C is identifying implies that based on the reports, we can uniquely identify the one malfunctioning processor or tell that everything is fine...