The metric dimension of a graph $ G $ is the minimum number of vertices in a subset $ S $
of the vertex set of $ G $ such that all other vertices are uniquely determined by their …

The advent of frequency-agile radios holds the potential for improving the utilization of
spectrum by allowing wireless systems to dynamically adapt their spectral footprint based on …

Assume that each vertex of a graph G is the possible location for an “intruder” such as a
thief, or a saboteur, a fire in a facility or some possible processor fault in a computer network …

How efficiently can we find an unknown graph using distance queries between its vertices?
We assume that the unknown graph is connected, unweighted, and has bounded degree …

A locating-dominating set of an undirected graph is a subset of vertices S such that S is
dominating and for every u, v∉ S, the neighbourhood of u and v on S are distinct (ie N (u)∩ …

We model a problem about networks built from wireless devices using identifying and
locating–dominating codes in unit disk graphs. It is known that minimizing the size of an …

Identifying codes were defined to model fault diagnosis in multiprocessor systems. They are
also used for the design of indoor detection systems based on wireless sensor networks …

An identifying code is a subset of vertices of a graph such that each vertex is uniquely
determined by its neighbourhood within the identifying code. If $\M (G) $ denotes the …

The problem of the r-identifying code of a cycle Cn has been solved totally when n is even.
Recently, S. Gravier et al. give the r-identifying code for the cycle Cn with the minimum …

We introduce the notion of watching systems in graphs, which is a generalization of that of
identifying codes. We give some basic properties of watching systems, an upper bound on …