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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
S. Balamurugan
Department of Mathematics, St. Xavier’s College, Palayamkottai - 627 002, India
Electrical & Electronics Engineering

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A note on isolate domination Ismail Sahul Hamid; S. Balamurugan; A. Navaneethakrishnan
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 4, No 1 (2016): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/egta.2016.4.1.8

Abstract

A set $S$ of vertices of a graph $G$ such that $\left\langle S\right\rangle$ has an isolated vertex is called an \emph{isolate set} of $G$. The minimum and maximum cardinality of a maximal isolate set are called the \emph{isolate number} $i_0(G)$ and the \emph{upper isolate number} $I_0(G)$ respectively. An isolate set that is also a dominating set (an irredundant set) is an $\emph{isolate dominating set} \ (\emph{an isolate irredundant set})$. The \emph{isolate domination number} $\gamma_0(G)$ and the \emph{upper isolate domination number} $\Gamma_0(G)$ are respectively the minimum and maximum cardinality of a minimal isolate dominating set while the \emph{isolate irredundance number} $ir_0(G)$ and the \emph{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.   
Co-Authors A. Navaneethakrishnan Ismail Sahul Hamid