Abstract
A set [Formula: see text] is a [Formula: see text]-point set dominating set (2-psd set) of a graph [Formula: see text] if for any subset [Formula: see text], there exists a nonempty subset [Formula: see text] containing at most two vertices such that the subgraph [Formula: see text] induced by [Formula: see text] is connected. The [Formula: see text]-point set domination number of [Formula: see text], denoted by [Formula: see text], is the minimum cardinality of a 2-psd set of [Formula: see text]. In this paper, we determine the lower bounds and an upper bound on [Formula: see text] of a graph. We also characterize extremal graphs for the lower bounds and identify some well-known classes of both separable and nonseparable graphs attaining the upper bound.
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