Hypergraph Coverings and their Zeta Functions

Abstract

Let $H$ be a finite hypergraph. The concept of hypergraph coverings over $H$ is introduced, and we can generate all hypergraph coverings by permutation voltage assignments of the edge-colored graph or the incidence graph of $H$. Consequently, we show two explicit decomposition formulae for the zeta function of any hypergraph covering $\overline{H}$ over $H$ which indicates that the zeta function of $H$ divides the zeta function of $\overline{H}$.