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The Zeta Functions of Dihypergraphs and Dihypergraph Coverings

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Abstract

As the generalization of the digraph, the directed hypergraph (dihypergraph), denoted by \({H}\), is considered in this paper. First, we introduce the notions of the zeta function of \({H}\) and dihypergraph coverings over \({H}\). Next, several expressions for the zeta function of \({H}\) are given, and all dihypergraph coverings over \({H}\) are generated by permutation voltage assignments on the incidence bipartite digraph or the edge-colored digraph of \({H}\). Final, we derive two explicit decomposition formulae for the zeta function of any dihypergraph covering \(\overline{{H}}\) over \({H}\), which turn out that the zeta function of \({H}\) divides the zeta function of \(\overline{{H}}\).

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Acknowledgements

This project is supported by the National Natural Science Foundation of China (Nos. 11971164, 12001185, 12001186), the Natural Science Foundation of Hunan Province, China (No. 2019JJ50173), and the Scientific Research Fund of Hunan Province Education Department (Nos. 19B313, 20C0520). The authors would like to thank the anonymous referees for their valuable comments and careful reviewing of this paper.

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Authors and Affiliations

  1. College of Science, Hunan University of Technology and Business, Changsha, 410205, Hunan, China

    Deqiong Li & Yunhua Liao

  2. Key Laboratory of Hunan Province for Statistical Learning and Intelligent Computation, Hunan University of Technology and Business, Changsha, 410205, Hunan, China

    Deqiong Li & Yunhua Liao

  3. College of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, China

    Yaoping Hou

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  1. Deqiong Li
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  2. Yaoping Hou
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  3. Yunhua Liao
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Correspondence to Yaoping Hou.

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Communicated by Xueliang Li.

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Li, D., Hou, Y. & Liao, Y. The Zeta Functions of Dihypergraphs and Dihypergraph Coverings. Bull. Malays. Math. Sci. Soc. 45, 399–415 (2022). https://doi.org/10.1007/s40840-021-01199-4

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