Trees having domination number equal to {K2}-isolation number

• Adriana Dapena ^[1] ; Magdalena Lemańska ^[2] ; María José Souto-Salorio ^[1] ; Francisco Vazquez Araujo ^[1]
  1. [1] Universidade da Coruña

     Universidade da Coruña

     A Coruña, España

     
  2. [2] Gdańsk University of Technology

     Gdańsk University of Technology

     Gdańsk, Polonia

     
• Localización: Discrete Mathematics Days 2022 / coord. por Luis Felipe Tabera Alonso, 2022, ISBN 978-84-19024-02-2, págs. 286-290
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let T = (VT , ET ) be a tree with n =| VT |≥ 3 vertices. A subset S ⊆ VT is calleddominating set if VT − NT [S] = ∅, where NT [S] denotes the closed neighborhood of thesubset S. The minimum cardinality of a dominating set is the domination number and it isdenoted by γ(T). We say W ⊆ VT is an {K2}−isolating set in T if the graph induced byVT − NT [W] contains no edges. The minimum cardinality of a {K2}−isolating set is theisolation number of T and it is denoted by ι(T). In this paper we give different equivalentcharacterizations of trees such that γ(T) = ι(T). Moreover, we focus our attention on treesthat verify ι(T) = n3. We show they form a subfamily of those for which γ(T) = ι(T) holds.