Graphs Defined on Rings: A Review

Title

Graphs Defined on Rings: A Review

Creator

Madhumitha S.; Naduvath S.

Description

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. 2023 by the authors.

Source

Mathematics, Vol-11, No. 17

Date

2023-01-01

Publisher

Multidisciplinary Digital Publishing Institute (MDPI)

Subject

absorption Cayley; divisor Cayley graphs; Euler totient Cayley graphs; involutory Cayley graphs; mixed unitary Cayley graphs; nilpotent Cayley graphs; quadratic residue Cayley graphs; unit graphs; unitary addition Cayley graphs; unitary Cayley graphs; zero-divisor Cayley graphs

Coverage

Madhumitha S., Department of Mathematics, CHRIST (Deemed to Be University), Bangalore, 560029, India; Naduvath S., Department of Mathematics, CHRIST (Deemed to Be University), Bangalore, 560029, India

Rights

All Open Access; Gold Open Access; Green Open Access

Relation

ISSN: 22277390

Format

Online

Language

English

Type

Review

Identifier

https://doi.org/10.3390/math11173643

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85176430260&doi=10.3390%2fmath11173643&partnerID=40&md5=f0fe506f07ad5b8cf416819c4b88ac4a