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Planar Graphs under Pythagorean Fuzzy Environment

Author

Listed:
  • Muhammad Akram

    (Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan)

  • Jawaria Mohsan Dar

    (Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan)

  • Adeel Farooq

    (Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54590, Pakistan)

Abstract

Graph theory plays a substantial role in structuring and designing many problems. A number of structural designs with crossings can be found in real world scenarios. To model the vagueness and uncertainty in graphical network problems, many extensions of graph theoretical ideas are introduced. To deal with such uncertain situations, the present paper proposes the concept of Pythagorean fuzzy multigraphs and Pythagorean fuzzy planar graphs with some of their eminent characteristics by investigating Pythagorean fuzzy planarity value with strong, weak and considerable edges. A close association is developed between Pythagorean fuzzy planar and dual graphs. This paper also includes a brief discussion on non-planar Pythagorean fuzzy graphs and explores the concepts of isomorphism, weak isomorphism and co-weak isomorphism for Pythagorean fuzzy planar graphs. Moreover, it presents a problem that shows applicability of the proposed concept.

Suggested Citation

  • Muhammad Akram & Jawaria Mohsan Dar & Adeel Farooq, 2018. "Planar Graphs under Pythagorean Fuzzy Environment," Mathematics, MDPI, vol. 6(12), pages 1-28, November.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:12:p:278-:d:185352
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    References listed on IDEAS

    as
    1. Noura Alshehri & Muhammad Akram, 2014. "Intuitionistic Fuzzy Planar Graphs," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-9, August.
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    Cited by:

    1. Amna Habib & Muhammad Akram & Adeel Farooq, 2019. "q -Rung Orthopair Fuzzy Competition Graphs with Application in the Soil Ecosystem," Mathematics, MDPI, vol. 7(1), pages 1-33, January.

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