All the results are "correct", but it is the periodic you want.
When you set the boundary condition to be non-periodic, there is no mirror atoms in the other cells, and hence you are effectively creating a 1D system,
and with a perfect 1D system you get a perfect step transmission spectrum.
If you want the to model the graphene bulk properties you need to make the structure periodic, and therefore in your case you should choose periodic in the a-axises. What you choose in the b-axis shouldn't really matter in this simulation, however I would go with Neumann.