  We study theoretically the minimal conductivity of monolayer graphene in the
presence of Rashba spin-orbit coupling. The Rashba spin-orbit interaction
causes the low-energy bands to undergo trigonal-warping deformation and for
energies smaller than the Lifshitz energy, the Fermi circle breaks up into
parts, forming four separate Dirac cones. We calculate the minimal conductivity
for an ideal strip of length $L$ and width $W$ within the Landauer--B\"uttiker
formalism in a continuum and in a tight binding model. We show that the minimal
conductivity depends on the relative orientation of the sample and the probing
electrodes due to the interference of states related to different Dirac cones.
We also explore the effects of finite system size and find that the minimal
conductivity can be lowered compared to that of an infinitely wide sample.
