The Zeta Function of a Hypergraph

Details The Zeta Function of a Hypergraph The Zeta Function of a Hypergraph

2006-08-30

arxiv.org/abs/math/0608761v1

Mathematics

Number Theory

24 pages, 6 figures

Scientific paper

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\'e. 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.

Affiliated with

Also associated with

No associations

Rating

The Zeta Function of a Hypergraph does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Zeta Function of a Hypergraph, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Zeta Function of a Hypergraph will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-74584