  Apropos to the growing interest in the study of long-range interactions which
for their applications in cold atom physics, we have performed theoretical
calculation for the two-dipole $C_6$ and three-dipole $C_9$ dispersion
coefficients involving alkaline-earth atoms with alkaline-earth atoms and
alkaline-earth ions. The $C_6$ and $C_9$ coefficients are expressed in terms of
the dynamic dipole polarizabilities, which are calculated using relativistic
methods. Thereafter, the calculated $C_6$ coefficients for the considered
alkaline-earth atoms among themselves are compared with the previously reported
values. Due to unavailability of any other earlier theoretical or experimental
results, for the $C_6$ coefficients for alkaline-earth atoms with
alkaline-earth ions and the $C_9$ coefficients, we have performed separate
fitting calculations and compared. Our calculations match in an excellent
manner with the fitting calculations. We have also reported the oscillator
strengths for the leading transitions and static dipole polarizabilities for
the ground states of the alkaline-earth ions, i.e., Mg$^+$, Ca$^+$, Sr$^+$, and
Ba$^+$ as well as the alkaline-earth atoms, i.e., Mg, Ca, Sr, and Ba. These,
when compared with the available experimental results, show good agreement.
