A note on isolate domination - Ismail Sahul Hamid; S. Balamurugan; A. Navaneethakrishnan (Electronic Journal of Graph Theory and Applications (EJGTA), 2016)
A set $S$ of vertices of a graph $G$ such that $\left\langle S\right\rangle$ has an isolated vertex is called an isolate set of $G$. The minimum and maximum cardinality of a maximal isolate set are called the isolate number $i_0(G)$ and the upper isolate number $I_0(G)$ respectively. An isolate set that is also a dominating set (an irredundant set) is an $isolate dominating set \ (an isolate irredundant set)$. The isolate domination number $γ_0(G)$ and the upper isolate domination number $Γ_0(G)$ are respectively the minimum and maximum cardinality of a minimal isolate dominating set while the isolate irredundance number $ir_0(G)$ and the upper isolate irredundance number $IR_0(G)$ are the minimum and maximum cardinality of a maximal isolate irredundant set of $G$. The notion of isolate domination was introduced in \cite{sb} and the remaining were introduced in \cite{isrn}. This paper further extends a study of these parameters.