Graphs Defined on Rings: A Review

S. Madhumitha and Sudev Naduvath ()
Additional contact information
S. Madhumitha: Department of Mathematics, CHRIST (Deemed to Be University), Bangalore 560029, India
Sudev Naduvath: Department of Mathematics, CHRIST (Deemed to Be University), Bangalore 560029, India

Mathematics, 2023, vol. 11, issue 17, 1-80

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; zero-divisor Cayley graphs; mixed unitary Cayley graphs; divisor Cayley graphs; involutory Cayley graphs; quadratic residue Cayley graphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/17/3643/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/17/3643/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:17:p:3643-:d:1223498

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().