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Graphs Defined on Rings: A Review

Author

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  • 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)

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.

Suggested Citation

  • S. Madhumitha & Sudev Naduvath, 2023. "Graphs Defined on Rings: A Review," Mathematics, MDPI, vol. 11(17), pages 1-80, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3643-:d:1223498
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    References listed on IDEAS

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    1. González-Arévalo, Bárbara & Palacios, José Luis, 1999. "Expected hitting times for random walks on weak products of graphs," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 33-39, May.
    2. Palacios, José Luis & Renom, José Miguel & Berrizbeitia, Pedro, 1999. "Random walks on edge-transitive graphs (II)," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 25-32, May.
    3. Obaidullah Wardak & Ayushi Dhama & Deepa Sinha, 2022. "On Some Properties of Addition Signed Cayley Graph Σ n ∧," Mathematics, MDPI, vol. 10(19), pages 1-11, September.
    4. Deepa Sinha & Obaidullah Wardak & Ayushi Dhama, 2022. "On Some Properties of Signed Cayley Graph S n," Mathematics, MDPI, vol. 10(15), pages 1-10, July.
    5. Palacios, JoséLuis & Renom, JoséMiguel, 1998. "Random walks on edge transitive graphs," Statistics & Probability Letters, Elsevier, vol. 37(1), pages 29-34, January.
    6. Liu, Xiaogang & Li, Binlong, 2016. "Distance powers of unitary Cayley graphs," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 272-280.
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