Let G=(V, E) be an undirected graph and C a subset of vertices. If the sets Br (v)∩ C, v∈ V
(respectively, v∈ V⧹ C), are all nonempty and different, where Br (v) denotes the set of all …

We consider the problems of finding optimal identifying codes,(open) locating-dominating
sets and resolving sets (denoted Identifying Code,(Open) Open Locating-Dominating Set …

Abstract Let $ G=(V, E) $ be a connected undirected graph and $ S $ a subset of vertices. If
for all vertices $ v\in V $, the sets $ B_r (v)\cap S $ are all nonempty and different, where …

An identifying code C is a subset of the vertices of the square grid \mathbbZ^2 with the
property that for each element v of \mathbbZ^2, the collection of elements from C at a …

Identifying codes are designed for locating faulty processors in multiprocessor systems. In
this paper we consider a natural extension of this problem and introduce strongly identifying …

Let G=(V, A) be a directed, asymmetric graph and C a subset of vertices, and let B/sub r//sup-
/(v) denote the set of all vertices x such that there exists a directed path from x to v with at …

The main topic of this paper is motivated by a localization problem in cellular networks.
Given a graph G we want to localize a walking agent by checking his distance to as few …

Let G=(V, E) be a graph and let r≥ 1 be an integer. For a set D⊆ V, define Nr [x]={y∈ V: d (x,
y)≤ r} and Dr (x)= Nr [x]∩ D, where d (x, y) denotes the number of edges in any shortest …

An identifying code of a graph G is a dominating set C such that every vertex x of G is
distinguished from other vertices by the set of vertices in C that are at distance at most 1 from …

Fault 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 …