Consider a connected undirected graph G=(V, E), a subset of vertices C⊆ V, and an integer
r≥ 1; for any vertex v∈ V, let Br (v) denote the ball of radius r centered at v, ie, 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 …

A set of vertices in a graph is (a) a dominating set if every vertex of Ò has a neighbor in,(b) a
locating-dominating set if for every two vertices Ù Ú of Ò the sets Æ (Ù) and Æ (Ú) are non …

We consider the problems of finding optimal identifying codes,(open) locating–dominating
sets and resolving sets of an interval or a permutation graph. In these problems, one asks to …

In this paper we deal with identifying codes in cycles. We show that for all r≥ 1, any r-
identifying code of the cycle Cn has cardinality at least gcd (2r+ 1, n)⌈ n2gcd (2r+ 1, n)⌉ …

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 …

Let G be a finite undirected graph with vertex set V (G). If v∈ V (G), let N [v] denote the
closed neighbourhood of v, ie v itself and all its adjacent vertices in G. An identifying code in …

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 …

An identifying code C of a graph G is a dominating set of G such that any two distinct vertices
of G have distinct closed neighborhoods within C. These codes have been widely studied for …