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A Novel Description of Some Concepts in Interval‐Valued Intuitionistic Fuzzy Graph with an Application

Author

Listed:
  • Xiaoli Qiang
  • Saeed Kosari
  • Xiang Chen
  • Ali Asghar Talebi
  • Ghulam Muhiuddin
  • Seyed Hossein Sadati

Abstract

Covering, matching, and domination are the basic concepts in graphs that play a decisive role in the properties of graphs. Calculating these parameters is one of the difficulties in fuzzy graphs when it is not possible to accurately determine the values of the vertices of a graph. The interval‐valued intuitionistic fuzzy graph (IVIFG) is one of the fuzzy graphs which can play an important role in solving uncertain problems in different sciences such as psychology, biological sciences, medicine, and social networks. The necessity of using a range of value instead of one number caused them to help researchers in optimizing and saving time and cost. In this study, we introduce some of the specific concepts such as covering, matching, and paired domination using strong arc or effective edges by giving appropriate examples. In addition, we have calculated strong node covering number, strong independent number, and other parameters of complete bipartite IVIFGs with several examples. Finally, we have presented an application of IVIFG in social networks.

Suggested Citation

  • Xiaoli Qiang & Saeed Kosari & Xiang Chen & Ali Asghar Talebi & Ghulam Muhiuddin & Seyed Hossein Sadati, 2022. "A Novel Description of Some Concepts in Interval‐Valued Intuitionistic Fuzzy Graph with an Application," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:2412012
    DOI: 10.1155/2022/2412012
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    References listed on IDEAS

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    1. Naeem Jan & Kifayat Ullah & Tahir Mahmood & Harish Garg & Bijan Davvaz & Arsham Borumand Saeid & Said Broumi, 2019. "Some Root Level Modifications in Interval Valued Fuzzy Graphs and Their Generalizations Including Neutrosophic Graphs," Mathematics, MDPI, vol. 7(1), pages 1-22, January.
    2. Zheng Kou & Saeed Kosari & Maryam Akhoundi & Lazim Abdullah, 2021. "A Novel Description on Vague Graph with Application in Transportation Systems," Journal of Mathematics, Hindawi, vol. 2021, pages 1-11, December.
    3. Muhammad Akram & Noura Omair Alshehri & Wieslaw A. Dudek, 2013. "Certain Types of Interval‐Valued Fuzzy Graphs," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    4. Jun Wang & Changfeng Ge & Dong Sun Lee & Michael A. Sek & Vanee Chonhenchob, 2013. "Mathematical Problems in Packaging Engineering," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-2, November.
    5. Muhammad Akram & Noura Omair Alshehri & Wieslaw A. Dudek, 2013. "Certain Types of Interval-Valued Fuzzy Graphs," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-11, October.
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