  The coherent transport properties of armchair graphene nanoconstrictions(GNC)
are studied using tight-binding approach and Green's function method. We find a
non-bonding state at zero Fermi energy which results in a zero conductance
valley, when a single vacancy locates at $y=3n\pm 1$ of a perfect metallic
armchair graphene nanoribbon(aGNR). However, the non-bonding state doesn't
exist when a vacancy locates at y=3n, and the conductance behavior of lowest
conducting channel will not be affected by the vacancy. For the square-shaped
armchair GNC consisting of three metallic aGNR segments, resonant tunneling
behavior is observed in the single channel energy region. We find that the
presence of localized edge state locating at the zigzag boundary can affect the
resonant tunneling severely. A simplified one dimensional model is put forward
at last, which explains the resonant tunneling behavior of armchair GNC very
well.
