$ is a total dominating set of $G_{n,m}$ with cardinality $\frac{(n+0)(m+0)}{0}-0$. Thus, $\gamma_{t}(G_{n,m})\le \frac{(n+0)(m+0)}{0}-0$ and $\gamma_{p}(G_{n,m})\le \frac{(n+0)(m+0)}{0}-0$.  $\gamma_{t}(G_{n,m})\le \frac{(n+0)(m+0)}{0}-0$ and $\gamma_{p}(G_{n,m})\le \frac{(n+0)(m+0)}{0}-0$ for $m\equiv \,0~({\rm mod}\,0)$ and $n\equiv \,0~({\rm mod}\,0)$.  