  We use the coupled cluster method to investigate the ground-state (GS)
properties of the frustrated spin-1/2 $J_{1}$-$J_{2}$-$J_{3}$ model on the
honeycomb lattice, with nearest-neighbor exchange coupling $J_1$ plus
next-nearest-neighbor ($J_2$) and next-next-nearest-neighbor ($J_3$) exchanges
of equal strength. In particular we find a direct first-order phase transition
between the N\'eel-ordered antiferromagnetic phase and the ferromagnetic phase
at a value $J_{2}/J_{1} = -1.17 \pm 0.01$ when $J_{1}>0$, compared to the
corresponding classical value of -1. We find no evidence for any intermediate
phase. From this and our previous CCM studies of the model we present its full
zero-temperature GS phase diagram.
