  In this paper, the average density of states (ADOS) with a binary alloy
disorder in disordered graphene systems are calculated based on the recursion
method. We observe an obvious resonant peak caused by interactions with
surrounding impurities and an anti-resonance dip in ADOS curves near the Dirac
point. We also find that the resonance energy (Er) and the dip position are
sensitive to the concentration of disorders (x) and their on-site potentials
(v). An linear relation, not only holds when the impurity concentration is low
but this relation can be further extended to high impurity concentration regime
with certain constraints. We also calculate the ADOS with a finite density of
vacancies and compare our results with the previous theoretical results.
