Title: Enumeration of Graphs and the Characteristic Polynomial of the Hyperplane Arrangements $\mathcal{J}_n$,
Abstract: We give a complete formula for the characteristic polynomial of hyperplane
arrangements $\mathcal J_n$ consisting of the hyperplanes $x_i+x_j=1$, $x_k=0$,
$x_l=1$, $ 1\leq i, j, k, l\leq n$. The formula is obtained by associating
hyperplane arrangements with graphs, and then enumerating central graphs via
generating functions for the number of bipartite graphs of given order, size
and number of connected components.