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On the Planarity of Graphs Associated with Symmetric and Pseudo Symmetric Numerical Semigroups

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  • Yongsheng Rao

    (Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China)

  • Muhammad Ahsan Binyamin

    (Department of Mathematics, GC University, Faisalabad 38000, Pakistan)

  • Adnan Aslam

    (Department of Natural Sciences and Humanities, University of Engineering and Technology, Lahore 54000, Pakistan)

  • Maria Mehtab

    (Department of Mathematics, GC University, Faisalabad 38000, Pakistan)

  • Shazia Fazal

    (Department of Mathematics, GC University, Faisalabad 38000, Pakistan)

Abstract

Let S ( m , e ) be a class of numerical semigroups with multiplicity m and embedding dimension e . We call a graph G S an S ( m , e ) -graph if there exists a numerical semigroup S ∈ S ( m , e ) with V ( G S ) = { x : x ∈ g ( S ) } and E ( G S ) = { x y ⇔ x + y ∈ S } , where g ( S ) denotes the gap set of S . The aim of this article is to discuss the planarity of S ( m , e ) -graphs for some cases where S is an irreducible numerical semigroup.

Suggested Citation

  • Yongsheng Rao & Muhammad Ahsan Binyamin & Adnan Aslam & Maria Mehtab & Shazia Fazal, 2023. "On the Planarity of Graphs Associated with Symmetric and Pseudo Symmetric Numerical Semigroups," Mathematics, MDPI, vol. 11(7), pages 1-11, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1681-:d:1112990
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    References listed on IDEAS

    as
    1. Muhammad Ahsan Binyamin & Hafiz Muhammad Afzal Siddiqui & Nida Munawar Khan & Adnan Aslam & Yongsheng Rao, 2019. "Characterization of Graphs Associated with Numerical Semigroups," Mathematics, MDPI, vol. 7(6), pages 1-8, June.
    2. Ying Wang & Muhammad Ahsan Binyamin & Wajid Ali & Adnan Aslam & Yongsheng Rao, 2021. "Graphs Associated with the Ideals of a Numerical Semigroup Having Metric Dimension 2," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-6, February.
    3. Peng Xu & Muhammad Ahsan Binyamin & Adnan Aslam & Wajid Ali & Hasan Mahmood & Hao Zhou & Marco Fontana, 2020. "Characterization of Graphs Associated with the Ideal of Numerical Semigroups," Journal of Mathematics, Hindawi, vol. 2020, pages 1-6, September.
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