  We take a wide-angle view of the problem of monolayer graphene (MLG) where
spin-degeneracy lifting is assumed to be possible by wedging in the tunable
Rashba spin-orbit coupling(RSOC) and the sub-lattice staggered potential. We
next consider the AB-stacked bi-layer graphene (BLG) system (the A-carbon of
the upper sheet lying on top of the B-carbon of the lower one) and assume that
a perpendicular electric field is created by the external gates deposited on
the BLG surface. This system exhibits the occurrence of trigonal warping due to
a (skew) interlayer hopping leading to the well-known Lifshitz
transition(LT)[Y. Lemonik, I.L. Aleiner, C. Toke, and V.I. Fal'ko;
arXiv:1006.1399]. We do not observe the replication of the features associated
with BLG-LT in MLG in the presence of RSOC.
