  We investigate the properties of magnon edge states in a ferromagnetic
honeycomb lattice with armchair boundaries. In contrast with fermionic
graphene, we find novel edge states due to the missing bonds along the boundary
sites. After introducing an external on-site potential at the outermost sites
we find that the energy spectra of the edge states are tunable. Additionally,
when a non-trivial gap is induced, we find that some of the edge states are
topologically protected and also tunable. Our results may explain the origin of
the novel edge states recently observed in photonic lattices. We also discuss
the behavior of these edge states for further experimental confirmations
