2006/08/30 by Christopher Storm, Storm, Christopher K. · 1 citation
Computer Science · Mathematics · #05C38 (Primary) 11M41 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Limits and Structures in Graph Theory #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.math/0608761
openalex publication_date 2006/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Solé. Finally, we give an example to show how the generalized zeta function can be applied to graphs to distinguish non-isomorphic graphs with the same Ihara-Selberg zeta function.