Hokkaido Mathematical Journal

A Note on Vertex-transitive K\"ahler graphs

Yaermaimaiti TUERXUNMAIMAITI and Toshiaki ADACHI

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Abstract

In this paper we construct finite vertex-transitive K\"ahler graphs, which may be considered as discrete models of Hermitian symmetric spaces admitting K\"ahler magnetic fields. We give a condition on cardinality of the set of vertices and the principal and the auxiliary degrees for a vertex-transitive K\"ahler graphs. Also we give some examples of K\"ahler graphs corresponding typical vertex-transitive ordinary graphs.

Article information

Source
Hokkaido Math. J., Volume 45, Number 3 (2016), 419-433.

Dates
First available in Project Euclid: 7 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1478487618

Digital Object Identifier
doi:10.14492/hokmj/1478487618

Mathematical Reviews number (MathSciNet)
MR3568636

Zentralblatt MATH identifier
1350.05021

Subjects
Primary: 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)
Secondary: 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]

Keywords
K\"ahler graphs regular graphs vertex-transitive graphs complete graphs partition functions

Citation

TUERXUNMAIMAITI, Yaermaimaiti; ADACHI, Toshiaki. A Note on Vertex-transitive K\"ahler graphs. Hokkaido Math. J. 45 (2016), no. 3, 419--433. doi:10.14492/hokmj/1478487618. https://projecteuclid.org/euclid.hokmj/1478487618


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