Both electronic and magnetic properties have been studied for hexagonally bonded honeycomb ribbons consisting of B, N, and C atoms, with zigzag edges terminated by H atoms. We have used first-principles total-energy electronic-structure calculations within the local spin-density functional theory. The energy gap of BN ribbons is dominated by the edge states and it decreases monotonically with increasing ribbon width. For metallic BNC ribbons with different zigzag edges, C and BN or NB, the ground state becomes ferrimagnetic; this originates from the coexistence of the border state and the edge state.
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