  The functionalized graphene with induced superconductivity, Zeeman coupling,
and finite Rashba spin-orbit coupling is proposed to display topological
superconducting phases with Majorana end modes. We obtain the phase diagram of
bulk graphene and nanoribbon by calculating the Chern number, band structure
and wavefunction. The electron doping in graphene, magnetic field and
strain-induced pseudomagnetic field can result in the topological phase
transition. Moreover, it is interested to note that strain has negative
influence on the stability of topological nontrivial phase either uniform or
nonuniform, destroying the existence of Majorana fermion, which provides a new
way to transfer, create and fuse Majorana fermions. Some experimental schemes
are also introduced to tailor functionalized graphene, generating various
devices applied in topological quantum computation.
