Geodesic
The zeta function of a hypergraph
The electronic journal of combinatorics, Tome 13 (2006)
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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.
DOI : 10.37236/1110
Classification : 05C65, 11M41
Mots-clés : Ihara-Selberg zeta function, Riemann hypothesis, Ramanujan 
@article{10_37236_1110,
     author = {Christopher K. Storm},
     title = {The zeta function of a hypergraph},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1110},
     zbl = {1112.05072},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1110/}
}
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Christopher K. Storm. The zeta function of a hypergraph. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1110

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