  The shock structure in a binary mixture of polyatomic Eulerian gases with
different degrees of freedom of a molecule is studied based on the
multi-temperature model of rational extended thermodynamics. Since the system
of field equations is hyperbolic, the shock-structure solution is not always
regular, and discontinuous parts (sub-shocks) can be formed. For given values
of the mass ratio and the specific heats of the constituents, we identify the
possible sub-shocks as the Mach number $M_0$ of the shock wave and the
concentration $c$ of the constituents change. In the plane $(c,M_0)$, we
identify the possible regions for the sub-shock formation. The analysis is
obtained to verify when the velocity of the shock wave meets a characteristic
velocity in the unperturbed or perturbed equilibrium states that gives a
necessary condition for the sub-shock formation. The condition becomes
necessary and sufficient when the velocity of the shock becomes greater than
the maximum characteristic velocity in the unperturbed state. Namely, the
regions with no sub-shocks, a sub-shock for only one constituent, or sub-shocks
for both constituents are comprehensively classified. The most interesting case
is that the lighter molecule has more degrees of freedom than that of the heavy
one. In this situation, the topology of the various regions becomes different.
We also solve the system of the field equations numerically using the
parameters in the various regions and confirm whether the sub-shocks emerge or
not. Finally, the relationship between an acceleration wave in a constituent
and the sub-shock in the other constituent is explicitly derived.
