Point set domination with reference to degree

R Poovazhaki, V Swaminathan


E.Sampathkumar et al introduced \cite{Es1} the concept of point set domination number of a graph. A set $D \subseteq V(G)$ is said to be a point set dominating set (psd set), if for every $S\subseteq V - D$ there exists a vertex $u \in D$ such that the subgraph $\left\langle S \cup\left\{u\right\}\right\rangle$ induced by $S \cup \left\{u\right\}$ is connected. The minimum cardinality of a psd set is called the point set domination number of $G$ and is denoted by $\gamma_{p}(G)$.In this paper psd sets are analysed with respect to the strong \cite{Es4} domination parameter for separable graphs. The characterization of separale graphs with equal psd number and spsd number is derived.

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