  In this paper, we count the number of independent sets of a type of graph
$G(\mathcal{A},q)$ associated to some hyperplane arrangement $\mathcal{A}$,
which is a generalization of the construction of graphical arrangements. We
show that when the parameters of $\mathcal{A}$ satisfy certain conditions, the
number of independent sets of the disjoint union
$G(\mathcal{A},q_1)\cup\cdots\cup G(\mathcal{A},q_s)$ depends only on the
coefficients of $\mathcal{A}$ and the total number of vertices $\sum_i q_i$
when $q_i$'s are powers of large enough prime numbers. In addition it is
independent of the coefficients as long as $\mathcal{A}$ is central and the
coefficients are multiplicatively independent.
