On Cayley graphs of algebraic structures

TL;DR

This paper provides simple graph-theoretic characterizations of Cayley graphs for various algebraic structures, including monoids, groups, and quasigroups, and demonstrates their effectiveness for finite degree end-regular graphs.

Contribution

It introduces new characterizations of Cayley graphs for multiple algebraic structures and applies them to finite degree end-regular graphs.

Findings

Characterizations are effective for finite degree end-regular graphs.

Unified approach for various algebraic structures.

Simplifies understanding of Cayley graph structures.

Abstract

We present simple graph-theoretic characterizations of Cayley graphs for left-cancellative monoids, groups, left-quasigroups and quasigroups. We show that these characterizations are effective for the end-regular graphs of finite degree.