CERTIFIED 2-DOMINATING SETS IN GRAPHS

Source abstract

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.