Let G(V,E) be a simple, undirected graph. An identifying code on G is a vertex-subset C ⊆ V such that B(v) ∩ C is non-empty and distinct for each vertex v ∈ V , where B(v) is a ball about v. Motivated by applications to fault diagnosis in multiprocessor arrays, a number of researchers have considered the problem of constructing identifying codes of minimum density on various two-dimensional lat...

An identifying code is a subset of vertices of a graph with the property that each vertex is uniquely determined (identified) by its nonempty neighbourhood within the identifying code. When only vertices out of the code are asked to be identified, we get the related concept of a locating-dominating set. These notions are closely related to a number of similar and well-studied concepts such as t...

v Combinatorial and algorithmic aspects of identifying codes in graphs Abstract: An identifying code is a set of vertices of a graph such that, on the one hand, each vertex out of the code has a neighbour in the code (the domination property), and, on the other hand, all vertices have a distinct neighbourhood within the code (the separation property). In this thesis, we investigate combinatoria...

We call a subset C of vertices of a graph G a (1,≤ l)-identifying code if for all subsets X of vertices with size at most l, the sets {c ∈ C|∃u ∈ X, d(u, c) ≤ 1} are distinct. The concept of identifying codes was introduced in 1998 by Karpovsky, Chakrabarty and Levitin. Identifying codes have been studied in various grids. In particular, it has been shown that there exists a (1,≤ 2)-identifying...

We call a subset C of vertices of a graph G a (1,≤ l)-identifying code if for all subsets X of vertices with size at most l, the sets {c ∈ C|∃u ∈ X, d(u, c) ≤ 1} are distinct. The concept of identifying codes was introduced in 1998 by Karpovsky, Chakrabarty and Levitin. Identifying codes have been studied in various grids. In particular, it has been shown that there exists a (1,≤ 2)-identifying...

An identifying code of a graph is a subset of its vertices such that every vertex of the graph is uniquely identified by the set of its neighbours within the code. We study the edge-identifying code problem, i.e. the identifying code problem in line graphs. If γID(G) denotes the size of a minimum identifying code of an identifiable graph G, we show that the usual bound γID(G) ≥ ⌈log2(n+1)⌉, whe...