  We evaluate separation dependent van der Waal dispersion ($C_3$) coefficients
for the interactions of the Li, Na, K and Rb alkali atoms with a graphene layer
and with a single walled carbon nanotube (CNT) using the hydrodynamic and Dirac
models. The results from both the models are evaluated using accurate values of
the dynamic polarizabilities of the above atoms. Accountability of these
accurate values of dynamical polarizabilities of the alkali atoms in
determination of the above $C_3$ coefficients are accentuated by comparing them
with the coefficients evaluated using the dynamic dipole polarizabilities
estimated from the single oscillator approximation which are typically employed
in the earlier calculations. For practical description of the atom-surface
interaction potentials the radial dependent $C_3$ coefficients are given for a
wide range of separation distances between the ground states of the considered
atoms and the wall surfaces and also for different values of nanotube radii.
The coefficients for the graphene layer are fit to a logistic function
dependent on the separation distance. For CNT, we have carried out a paraboloid
kind of fit dependent on both the separation distances and radii of the CNT.
These fitted functions,with the list of fitting parameters, can be used to
extrapolate the interaction potentials between the considered alkali atoms and
the graphene layer or CNT surface conveniently at the given level of accuracy.
