The Characteristic polynomials of semigeneric graphical arrangements

The purpose of this paper is twofold. Firstly, we generalize the notion of semigeneric braid arrangement to semigeneric graphical arrangement. Secondly, we give a formula for the characteristic polynomial of the semigeneric graphical arrangement ${\mathcal{S}}_G:=\{x_i-x_j=a_i:ij\in E(G),1\le i<j\le n\}$, where $a_i{}^{\prime }\mathrm{s}$ are generic. The formula is obtained by characterizing central subarrangements of ${\mathcal{S}}_G$ via the corresponding graph $G$.