  A recently derived formula for complex conductivity of the monolayer graphene
is analyzed. We show that the real and imaginary parts in this formula obey the
Kramers and Kronig dispersion relations which are a good test for validity of
the formula for complex conductivity of monolayer graphene. We consider also an
additional test for this formula, sensitive to the integral characteristic of
the conductance such as the famous f sum rule. We write it in the two
dimensional form and show that it fulfils identically if we admit the cyclotron
mass as an effective one and take the principal value of the integral. We find
a deep relation between the graphene complex optical conductivity singularities
and electrons Zitterbewegung in graphene. Namely, the value of Zitterbewegung
frequency is related with the recently found magnitudes of the inductance L and
capacitance C by the Thomson formula.
