# Minimum sizes of identifying codes in graphs differing by one vertex

• Published 2012 in Cryptography and Communications

#### Abstract

Let G be a simple, undirected graph with vertex set V. For v ∈ V and r ≥ 1, we denote by B G,r (v) the ball of radius r and centre v. A set ${\cal C} \subseteq V$ is said to be an r-identifying code in G if the sets $B_{G,r}(v)\cap {\cal C}$ , v ∈ V, are all nonempty and distinct. A graph G admitting an r-identifying code is called r-twin-free, and in this… (More)
DOI: 10.1007/s12095-012-0078-2