Affiliation:
1. Department of Mathematics, CHRIST (Deemed to Be University), Bangalore 560029, India
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.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference304 articles.
1. Graphs of degree three with a given abstract group;Frucht;Can. J. Math.,1949
2. The power graph of a finite group;Cameron;Discrete Math.,2011
3. Commuting graphs of dihedral type groups;Raza;Appl. Math. E-Notes,2013
4. Comaximal factorization graphs in integral domains;Rehman;J. Prime Res. Math.,2013
5. Graphs and classes of finite groups;Cossey;Note Math.,2013