Maximum Size of a Minimum Watching System and the Graphs Achieving the Bound - Télécom Paris Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2012

Maximum Size of a Minimum Watching System and the Graphs Achieving the Bound

David Auger
  • Fonction : Auteur
  • PersonId : 952013
Irène Charon
  • Fonction : Auteur
  • PersonId : 845562
Olivier Hudry

Résumé

Let G = (V(G);E(G)) be an undirected graph. A watcher w of G is a couple w = (l(w), A(w)), where l(w) belongs to V(G) and A(w) is a set of vertices of G at distance 0 or 1 from l(w). If a vertex v belongs to A(w), we say that v is covered by w. Two vertices v1 and v2 in G are said to be separated by a set of watchers if the list of the watchers covering v1 is diff erent from that of v2. We say that a set W of watchers is a watching system for G if every vertex v is covered by at least one watcher w belonging to W, and every two vertices v1, v2 are separated by W. The minimum number of watchers necessary to watch G is denoted by w(G). We give an upper bound on w(G) for connected graphs of order n and characterize the trees attaining this bound, before studying the more complicated characterization of the connected graphs attaining this bound.
Fichier principal
Vignette du fichier
Watching_systems_ACHL_HAL_mars_2012.pdf (349.61 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00680690 , version 1 (19-03-2012)

Identifiants

  • HAL Id : hal-00680690 , version 1

Citer

David Auger, Irène Charon, Olivier Hudry, Antoine Lobstein. Maximum Size of a Minimum Watching System and the Graphs Achieving the Bound. 2012. ⟨hal-00680690⟩
162 Consultations
131 Téléchargements

Partager

Gmail Facebook X LinkedIn More