  Dirac electrons in clean graphene can mediate the interactions between two
localized magnetic moments. The functional form of the RKKY interaction in
pristine graphene is specified by two main features: (i) an atomic scale
oscillatory part determined by a wave vector $\vec Q$ connecting the two
valleys. Furthermore with doping another longer range oscillation appears which
arise from the existence of an extended Fermi surface characterized by a single
momentum scale $k_F$. (ii) $R^{\alpha}$ decay in large distances where the
exponent $\alpha=-3$ is a distinct feature of undoped Dirac sea (with a linear
dispersion relation) in two dimensions. In this work, we investigate the effect
of a few percent vacancies on the above properties. Depending on the doping
level, if the chemical potential lies on the linear part of the density of
states, the exponent $\alpha$ remains close to -3. Otherwise $\alpha$ reduces
towards more negative values which means that the combined effect of vacancies
and the randomness in their positions makes it harder for the carriers of the
medium to mediate the magnetic interaction. Addition of a few percent of
vacancies diminishes the atomic scale oscillations of the RKKY interaction
signaling the destruction of two-valley structure of the parent graphene
material. Surprisingly by allowing the chemical potential to vary, we find that
the longer-range oscillations expected to arise from the existence of a $k_F$
scale in the vacant graphene are absent. This may indicate possible non-Fermi
liquid behavior by "alloying" graphene with vacancies. The complete absence of
oscillations in heavily vacant graphene can be considered an advantage for
applications as a uniform sign of the exchange interaction is desirable for
magnetic ordering.
