A note on quadrangular embedding of Abelian Cayley Graphs

TL;DR

This paper establishes a general lower bound for the genus of abelian Cayley graphs and constructs circulant graphs that attain this bound, advancing understanding of their topological properties.

Contribution

It provides a new lower bound for the genus of abelian Cayley graphs and demonstrates a family of circulant graphs that achieve this bound.

Findings

Derived a general lower bound for the genus of abelian Cayley graphs.

Constructed circulant graphs that reach the established genus bound.

Abstract

The genus graphs have been studied by many authors, but just a few results concerning in special cases: Planar, Toroidal, Complete, Bipartite and Cartesian Product of Bipartite. We present here a derive general lower bound for the genus of a abelian Cayley graph and construct a family of circulant graphs which reach this bound.