The conducting properties of various finite graphene ribbons and their junctions are investigated. These were found to depend strongly on their size and geometric features. Small arm-chair ribbons, when connected through tapered geometries, are found to exhibit very narrow conducting windows. No conductance is found through small armchair zigzag armchair ribbon junctions when connected via pentagon-heptagon defect lines. However, the conducting windows become broader as the size of the ribbons increases.
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