  Within the tunneling Hamiltonian formulation for the eight-component
spinors,the Josephson critical super-current has been calculated in a planar
superconductor-normal graphene-superconductor junction. Coupling between
superconductor regions and graphene is taken into account by a tunneling
Hamiltonian which contains two types of tunneling, intra-valley and
inter-valley tunneling. Within the present tunneling approach, we find that the
contributions of two kinds of tunneling to the critical super-current, are
completely separable. Therefore, it is possible to consider the effect of the
inter-valley tunnelings in the critical super-current. The incorporation of
these type of processes into the tunneling Hamiltonian, exposes a special
feature of the graphene Josephson junctions. The effect of inter-valley
tunneling appears in the length dependence plot of critical current in the form
of oscillations. We also present the results for temperature dependence of
critical super-current and compare with experimental results and other
theoretical calculations.
