Minimum sizes of identifying codes in graphs differing by one vertex

  • Authors:

  • Irène Charon;Iiro Honkala;Olivier Hudry;Antoine Lobstein

  • Affiliations:

  • Télécom ParisTech & CNRS - LTCI UMR 5141, Institut Téélécom, Paris Cedex 13, France 75634;Department of Mathematics and Statistics, University of Turku, Turku, Finland 20014;Télécom ParisTech & CNRS - LTCI UMR 5141, Institut Téélécom, Paris Cedex 13, France 75634;Télécom ParisTech & CNRS - LTCI UMR 5141, Institut Téélécom, Paris Cedex 13, France 75634

  • Venue:
  • Cryptography and Communications
  • Year:
  • 2013

Quantified Score

Hi-index 0.00

Visualization

Abstract

Let G be a simple, undirected graph with vertex set V. For v驴驴驴V and r驴驴驴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驴驴驴V, are all nonempty and distinct. A graph G admitting an r-identifying code is called r-twin-free, and in this case the size of a smallest r-identifying code in G is denoted by 驴 r (G). We study the following structural problem: let G be an r-twin-free graph, and G * be a graph obtained from G by adding or deleting a vertex. If G * is still r-twin-free, we compare the behaviours of 驴 r (G) and $\gamma_r(G^*)$ , establishing results on their possible differences and ratios.