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Exploring Graph Embedding Strategies for Co-Intersection Ideals in Commutative Rings

Author

Listed:
  • Turki Alsuraiheed

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Junaid Nisar

    (Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed) University, Lavale, Pune 412115, India)

Abstract

This research article examines the co-intersection graph of a commutative ring 𝒮 . The co-intersection graph Ω ( 𝒮 ) is defined as a simple graph where the vertices correspond to the non-trivial ideals of 𝒮 , and two distinct vertices I and J are adjacent if and only if I + J ≠ 𝒮 . In this study, we first classify the Artinian rings 𝒮 for which Ω ( 𝒮 ) is isomorphic to certain basic graphs, such as a unicycle, a split graph, or a threshold graph. Subsequently, we investigate the genus of Ω ( 𝒮 ) and identify the rings 𝒮 for which Ω ( 𝒮 ) represents a double-toroidal graph. Furthermore, we analyze the crosscap of Ω ( 𝒮 ) and determine the rings 𝒮 for which Ω ( 𝒮 ) corresponds to the projective plane or the Klein bottle. Lastly, we compute the book thickness of Ω ( 𝒮 ) for cases where the genus is at most one.

Suggested Citation

  • Turki Alsuraiheed & Junaid Nisar, 2026. "Exploring Graph Embedding Strategies for Co-Intersection Ideals in Commutative Rings," Mathematics, MDPI, vol. 14(9), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:14:y:2026:i:9:p:1404-:d:1926108
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