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

Adriana Dapena , Magdalena Lemanska , María José Souto Salorio, Francisco Vazquez Araujo

• 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.