In a graph G = (V, E), an identifying code of G (resp. a locating-dominating code of G) is a subset of vertices C ⊆ V such that N [v]∩C 6= ∅ for all v ∈ V , and N [u] ∩C 6= N [v]∩C for all u 6= v, u, v ∈ V (resp. u, v ∈ V r C), where N [u] denotes the closed neighbourhood of v, that is N [u] = N(u) ∪ {u}. These codes model fault-detection problems in multiprocessor systems and are also used for...

It is important for networks built from wireless sensors technology to have a functional location detection system. Identifying codes, first introduced to model fault diagnosis of multi-processor systems, have recently proved to be useful to address this question. We are interested in the situation where the area of communication of each sensor is modelled by a disk: thus we consider identifyin...

ÐFault diagnosis of multiprocessor systems motivates the following graph-theoretic definition. A subset C of points in an undirected graph G ˆ …V ;E† is called an identifying code if the sets B…v† \ C consisting of all elements of C within distance one from the vertex v are different. We also require that the sets B…v† \ C are all nonempty. We take G to be the infinite square lattice with diago...