  Linear conductance of junctions formed by graphene flakes with order of
nanometer-thick electrodes attached at the corners of the flakes is studied.
The explored structures have sizes up to 20000 atoms and the conductance is
studied as a function of applied gate voltage varied around the Fermi level.
The finding, obtained computationally, is that junctions formed by
armchair-edge flakes with the electrodes connected at the acute-angle corners
block the electron transport while only junctions with such electrodes at the
obtuse-angle corners tend to provide the high electrical conductance typical
for metallic GNRs. The finding in case of zig-zag edges is similar with an
exception of a relatively narrow gate voltage interval in which each studied
junction is highly conductive as mediated by the edge states. The contrast
between the conductive and insulating setups is typically several orders of
magnitude in terms of ratio of their conductances. Main results of the paper
remain to a large extent valid also in the presence of edge disorder.
