  We study the metastability of the ferromagnetic Ising model on a random
$r$-regular graph in the zero temperature limit. We prove that in the presence
of a small positive external field the time that it takes to go from the all
minus state to the all plus state behaves like ${\exp(\beta (r/2+
\mathcal{O}(\sqrt{r}))n)}$ when the inverse temperature
$\beta\rightarrow\infty$ and the number of vertices $n$ is large enough but
fixed. The proof is based on the so-called pathwise approach and bounds on the
isoperimetric number of random regular graphs.
