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

  1. Adriana Dapena 1
  2. Magdalena Lemańska 2
  3. María José Souto-Salorio 1
  4. Francisco Vazquez Araujo 1
  1. 1 Universidade da Coruña. España
  2. 2 Gdańsk University of Technology. Poland
Libro:
Discrete Mathematics Days 2022
  1. Luis Felipe Tabera Alonso (ed. lit.)

Editorial: Editorial de la Universidad de Cantabria ; Universidad de Cantabria

ISBN: 978-84-19024-02-2

Ano de publicación: 2022

Páxinas: 286-290

Tipo: Capítulo de libro

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Resumo

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.

Fonte de datos: Dialnet