CERTIFIED 2-DOMINATING SETS IN GRAPHS

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 \(\gamma_{2 \text { cer }}(G)-\gamma_{\text {cer }}(G)\) can be increased without bound, where \(\gamma_{2 \text { cer }}(G)\) and \(\gamma_{c e r}(G)\) 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.