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 Universidade da Coruña. España
- 2 Gdańsk University of Technology. Poland
- Luis Felipe Tabera Alonso (ed. lit.)
Publisher: Editorial de la Universidad de Cantabria ; Universidad de Cantabria
ISBN: 978-84-19024-02-2
Year of publication: 2022
Pages: 286-290
Type: Book chapter
Abstract
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.