Let G = (V,E) be a connected undirected graph and S a subset of vertices. If for all vertices v ∈ V , the sets Br(v) ∩ S are all nonempty and different, where Br(v) denotes the set of all points… (More)

Consider a connected undirected graph G = (V, E), a subset of verticesC ⊆ V , and an integer r ≥ 1; for anyvertexv ∈ V , let Br (v) denote the ball of radius r centered atv, i.e., the set of all… (More)

ÐFault diagnosis of multiprocessor systems motivates the following graph-theoretic definition. A subset C of points in an undirected graph G V ;E is called an identifying code if the sets B v \… (More)

Consider a connected undirected graph G = (V,E) and a subset of vertices C. If for all vertices v ∈ V , the sets Br(v) ∩ C are all nonempty and pairwise distinct, where Br(v) denotes the set of all… (More)

Vertices in Graphs G erard Cohen cohen@inf.enst.fr Iiro Honkala honkala@utu.fi Antoine Lobstein lobstein@inf.enst.fr Gilles Z emor zemor@infres.enst.fr Abstract Let G = (V;E) be an undirected graph.… (More)

A number of upper and lower bounds are obtained for K( n, R), the minimal number of codewords in any binary code of length n and covering radius R. Several new constructions are used to derive the… (More)

In an undirected graph G = (V; E) a subset C V is called an identifying code, if the sets B1 (v) \ C consisting of all elements of C within distance one from the vertex v are nonempty and diierent.… (More)