A Note on Vertex-transitive K\"ahler graphs

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.