On certain hyperplane arrangements and colored graphs

Abstract

We exhibit a one-to-one correspondence between $3$-colored graphs and subarrangements of certain hyperplane arrangements denoted ${\mathcal{J}}_n$, $n\in \mathbb{N}$. We define the notion of centrality of $3$-colored graphs which corresponds to the centrality of hyperplane arrangements. Via the correspondence, the characteristic polynomial ${\chi }_{{\mathcal{J}}_n}$ of ${\mathcal{J}}_n$ can be expressed in terms of the number of central $3$-colored graphs, and we compute ${\chi }_{{\mathcal{J}}_n}$ for $n=2,3$.

Cited by in corpus (2)

• Characteristic Polynomial of Certain Hyperplane Arrangements through Graph Theory
• Enumeration of Graphs and the Characteristic Polynomial of the Hyperplane Arrangements ${\mathcal{J}}_n$