Graphs Defined on Rings: A Review

Abstract

The study on graphs emerging from different algebraic structures such as groups, rings, fields, vector spaces, etc. is a prominent area of research in mathematics, as algebra and graph theory are two mathematical fields that focus on creating and analysing structures. There are numerous studies linking algebraic structures and graphs, which began with the introduction of Cayley graphs of groups. Several algebraic graphs have been defined on rings, a fast-growing area in the literature. In this article, we systematically review the literature on some variants of Cayley graphs that are defined on rings and highlight the properties and characteristics of such graphs, to showcase the research in this area.

Keywords

• unitary Cayley graphs
• Euler totient Cayley graphs
• unitary addition Cayley graphs
• unit graphs
• absorption Cayley
• nilpotent Cayley graphs