The Zeta Function of a Hypergraph

We generalize the Ihara-Selberg zeta function to hypergraphs in a natural way. Hashimoto's factorization results for biregular bipartite graphs apply, leading to exact factorizations. For (d, r)-regular hypergraphs, we show that a modified Riemann hypothesis is true if and only if the hypergraph is Ramanujan in the sense of Winnie Li and Patrick Sol

• Type: Journal
• Year: 2006
• Where: COMBINATORICS
• Authors: Christopher K. Storm
• Keywords: Biregular Bipartite Graphs, COMBINATORICS 2006, Ihara-Selberg Zeta Function, Zeta Function