  Largely motivated by a number of applications, the van der Waals dispersion
coefficients ($C_3$s) of the alkali ions (Li$^+$, Na$^+$, K$^+$ and Rb$^+$),
the alkaline-earth ions (Ca$^+$, Sr$^+$, Ba$^+$ and Ra$^+$) and the inert gas
atoms (He, Ne, Ar and Kr) with a graphene layer are determined precisely within
the framework of Dirac model. For these calculations, we have evaluated the
dynamic polarizabilities of the above atomic systems very accurately by
evaluating the transition matrix elements employing relativistic many-body
methods and using the experimental values of the excitation energies. The
dispersion coefficients are, finally, given as functions of the separation
distance of an atomic system from the graphene layer and the ambiance
temperature during the interactions. For easy extraction of these coefficients,
we give a logistic fit to the functional forms of the dispersion coefficients
in terms of the separation distances at the room temperature.
