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New Concepts in Intuitionistic Fuzzy Graph with Application in Water Supplier Systems

Author

Listed:
  • Zehui Shao

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

  • Saeed Kosari

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

  • Hossein Rashmanlou

    (Mazandaran Adib Institute of Higher Education, Sari 48175, Iran)

  • Muhammad Shoaib

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

Abstract

In recent years, the concept of domination has been the backbone of research activities in graph theory. The application of graphic domination has become widespread in different areas to solve human-life issues, including social media theories, radio channels, commuter train transportation, earth measurement, internet transportation systems, and pharmacy. The purpose of this paper was to generalize the idea of bondage set (BS) and non-bondage set (NBS), bondage number α ( G ) , and non-bondage number α k ( G ) , respectively, in the intuitionistic fuzzy graph (IFG). The BS is based on a strong arc (SA) in the fuzzy graph (FG). In this research, a new definition of SA in connection with the strength of connectivity in IFGs was applied. Additionally, the BS, α ( G ) , NBS, and α k ( G ) concepts were presented in IFGs. Three different examples were described to show the informative development procedure by applying the idea to IFGs. Considering the examples, some results were developed. Also, the applications were utilized in water supply systems. The present study was conducted to make daily life more useful and productive.

Suggested Citation

  • Zehui Shao & Saeed Kosari & Hossein Rashmanlou & Muhammad Shoaib, 2020. "New Concepts in Intuitionistic Fuzzy Graph with Application in Water Supplier Systems," Mathematics, MDPI, vol. 8(8), pages 1-17, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1241-:d:391753
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    References listed on IDEAS

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    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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    Cited by:

    1. P. Aruna Sri & N. Thamaraikannan & K. Loganathan & Dinesh Kumar Chaudhary, 2022. "Double Domination and Regular Domination in Intuitionistic Fuzzy Hypergraph," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    2. Xiaolong Shi & Maryam Akhoundi & A. A. Talebi & Masome Mojahedfar, 2023. "A Study on Regular Domination in Vague Graphs with Application," Advances in Mathematical Physics, John Wiley & Sons, vol. 2023(1).
    3. Annamalai Meenakshi & Obel Mythreyi & Robert Čep & Krishnasamy Karthik, 2024. "A Study on Optimizing the Maximal Product in Cubic Fuzzy Graphs for Multifaceted Applications," Mathematics, MDPI, vol. 12(10), pages 1-16, May.
    4. Peng Xu & Hao Guan & A. A. Talebi & M. Ghassemi & Hossein Rashmanlou, 2022. "Certain Concepts of Interval‐Valued Intuitionistic Fuzzy Graphs with an Application," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    5. Lian Chen & Aysha Khan & Maryam Akhoundi & A. A. Talebi & G. Muhiuddin & S. H. Sadati, 2022. "A Study on m‐Polar Interval‐Valued Intuitionistic Fuzzy Graphs with Application in Management," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    6. Tulat Naeem & Muhammad Kamran Jamil & Khawaja Muhammad Fahd & Abdu alAmeri, 2022. "Wiener Index of Intuitionistic Fuzzy Graphs with an Application to Transport Network Flow," Complexity, John Wiley & Sons, vol. 2022(1).

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