  The electronic properties of a particular class of domain walls in gapped
graphene are investigated. We show that they can support mid-gap states which
are localized in the vicinity of the domain wall and propagate along its
length. With a finite density of domain walls, these states can alter the
electronic properties of gapped graphene significantly. If the mid-gap band is
partially filled,the domain wall can behave like a one-dimensional metal
embedded in a semi-conductor, and could potentially be used as a single-channel
quantum wire.
