Abstract
Given a graph [Formula: see text] with no isolated vertices, let [Formula: see text] [Formula: see text] [Formula: see text] [Formula: see text] [Formula: see text] and [Formula: see text] denote the ev-domination number, the independent ev-domination number, the upper independent ev-domination number, the domination number, the paired-domination number and the upper paired-domination number, respectively. It is known that [Formula: see text] In this paper, we extend this inequality chain to involve the upper paired-domination number for arbitrary graphs [Formula: see text] with no isolated vertices as well as the domination number for trees. Moreover, we show that recognizing well ev-covered graphs (i.e., graphs [Formula: see text] with [Formula: see text]) is co-NP-complete, solving an open problem posed by Boutrig and Chellali.
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