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

被引：0

作者：

Toshiaki Adachi

Guanyuan Chen

机构：

[1] Nagoya Institute of Technology,Department of Mathematics

[2] Nagoya Institute of Technology,Division of Mathematics and Mathematical Science

[3] Renesas Electronic Co.,Automotive Business Unit

来源：

Graphs and Combinatorics | 2020年 / 36卷

关键词：

Kähler graphs; Vertex-transitive graphs; Adjacency operators; Bicolored paths; Zeta functions; 05C50; 53C55;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：933 / 958

页数：25