Bartholdi Zeta Functions for Hypergraphs

Iwao SATO

Abstract


Recently, Storm defined the Ihara-Selberg zeta function of a hypergraph, and gave two determinant expressions of it. We define the Bartholdi zeta function of a hypergraph, and present a determinant expression of it. Furthermore, we give a determinant expression for the Bartholdi zeta function of semiregular bipartite graph. As a corollary, we obtain a decomposition formula for the Bartholdi zeta function of some regular hypergraph.


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