Answer
See the detailed answer below.
Work Step by Step
Let's assume that each degree of freedom will contribute $\frac{1}{2} R$ to the molar-specific heat.
In a two-dimensional lattice, the motion of an atom is confined to two directions, hence the compression or stretching of molecular bonds occurs in two dimensions as well.
This yields 4 degrees of freedom which means that the molar-specific heat of graphene might be $2R$.
The atoms can also move slightly out of the plane, which adds another degree of freedom, and this out-of-plane motion induces bond stretching in a new manner, adding another degree of freedom.
Thus there are more than 4 degrees of freedom.
Recalling that the actual value of the molar-specific heat of graphene is 23.5 J/mol K which means that there are between 5 to 6 degrees of freedom, Not only 4.
