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Regular and Vertex-Transitive Kähler Graphs Having Commutative Principal and Auxiliary Adjacency Operators

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Abstract

A Kähler graph is a compound of two graphs having a common set of vertices and is a discrete model of a Riemannian manifold equipped with magnetic fields. In this paper we study selfadjointness of adjacency operators of Kähler graphs and express their zeta functions in terms of eigenvalues of their principal and auxiliary adjacency operators when they are commutative. Also, we construct finite vertex-transitive Kähler graphs satisfying the commutativity condition.

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Acknowledgements

The first author is partially supported by Grant-in-Aid for Scientific Research (C) (No. 16K05126), Japan Society for the Promotion of Sciences.

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  1. Guanyuan Chen

    Present address: Automotive Business Unit, Renesas Electronic Co., Kami-mizumoto, Kodaira, 187-8588, Japan

Authors and Affiliations

  1. Department of Mathematics, Nagoya Institute of Technology, Nagoya, 466-8555, Japan

    Toshiaki Adachi

  2. Division of Mathematics and Mathematical Science, Nagoya Institute of Technology, Nagoya, 466-8555, Japan

    Guanyuan Chen

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  1. Toshiaki Adachi
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  2. Guanyuan Chen
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Correspondence to Toshiaki Adachi.

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Adachi, T., Chen, G. Regular and Vertex-Transitive Kähler Graphs Having Commutative Principal and Auxiliary Adjacency Operators. Graphs and Combinatorics 36, 933–958 (2020). https://doi.org/10.1007/s00373-020-02151-2

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  • DOI: https://doi.org/10.1007/s00373-020-02151-2

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