Preprint Review Version 1 Preserved in Portico This version is not peer-reviewed

Graphs Defined on Rings: A Review

Version 1 : Received: 31 July 2023 / Approved: 1 August 2023 / Online: 2 August 2023 (02:24:55 CEST)

A peer-reviewed article of this Preprint also exists.

Madhumitha, S.; Naduvath, S. Graphs Defined on Rings: A Review. Mathematics 2023, 11, 3643. Madhumitha, S.; Naduvath, S. Graphs Defined on Rings: A Review. Mathematics 2023, 11, 3643.


The study on graphs emerging from different algebraic structures like groups, rings, fields, vector spaces, etc. is a prominent area of research in mathematics, as algebra and graph theory are two mathematical fields that focuses 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, which have huge-growing literature. In this article, we systematically review the literature on some variants of Cayley graphs that are defined on rings, to understand the research in this area.


Unitary Cayley Graphs; Euler Totient Cayley Graphs; Unitary Addition Cayley Graphs; Unit Graphs; Absorption Cayley graphs; Nilpotent Cayley Graphs; Zero-divisor Cayley Graphs; Mixed unitary Cayley Graphs; Divisor Cayley Graphs; Involutory Cayley Graphs; Quadratic Residue Cayley Graphs


Computer Science and Mathematics, Discrete Mathematics and Combinatorics

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