We introduce and investigate the concepts of certified 2-dominating sets and certified 2-domination numbers of a graph. Here, we give necessary and sufficient conditions for a graph to attain a specific value of the parameter. It is shown that the difference \(γ2 cer(G)-γcer(G)\) can be increased without bound, where \(γ2 cer(G)\) and \(γc e r(G)\) denote the certified 2-domination and certified domination numbers of \(G\), respectively. Some results on the concept for the join of two non-trivial graphs are also obtained.
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Sappari et al. (2026) studied this question.
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