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Certain Properties of Vague Graphs with a Novel Application

Author

Listed:
  • Yongsheng Rao

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

  • Saeed Kosari

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

  • Zehui Shao

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

Abstract

Fuzzy graph models enjoy the ubiquity of being present in nature and man-made structures, such as the dynamic processes in physical, biological, and social systems. As a result of inconsistent and indeterminate information inherent in real-life problems that are often uncertain, for an expert, it is highly difficult to demonstrate those problems through a fuzzy graph. Resolving the uncertainty associated with the inconsistent and indeterminate information of any real-world problem can be done using a vague graph (VG), with which the fuzzy graphs may not generate satisfactory results. The limitations of past definitions in fuzzy graphs have led us to present new definitions in VGs. The objective of this paper is to present certain types of vague graphs (VGs), including strongly irregular (SI), strongly totally irregular (STI), neighborly edge irregular (NEI), and neighborly edge totally irregular vague graphs (NETIVGs), which are introduced for the first time here. Some remarkable properties associated with these new VGs were investigated, and necessary and sufficient conditions under which strongly irregular vague graphs (SIVGs) and highly irregular vague graphs (HIVGs) are equivalent were obtained. The relation among strongly, highly, and neighborly irregular vague graphs was established. A comparative study between NEI and NETIVGs was performed. Different examples are provided to evaluate the validity of the new definitions. A new definition of energy called the Laplacian energy (LE) is presented, and its calculation is shown with some examples. Likewise, we introduce the notions of the adjacency matrix (AM), degree matrix (DM), and Laplacian matrix (LM) of VGs. The lower and upper bounds for the Laplacian energy of a VG are derived. Furthermore, this study discusses the VG energy concept by providing a real-time example. Finally, an application of the proposed concepts is presented to find the most effective person in a hospital.

Suggested Citation

  • Yongsheng Rao & Saeed Kosari & Zehui Shao, 2020. "Certain Properties of Vague Graphs with a Novel Application," Mathematics, MDPI, vol. 8(10), pages 1-25, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1647-:d:418376
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    Citations

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    Cited by:

    1. 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).
    2. Chang Wan & Fei Deng & Shitao Li & S. Omidbakhsh Amiri & A. A. Talebi & H. Rashmanlou, 2022. "[Retracted] Novel Concepts in Bipolar Fuzzy Graphs with Applications," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    3. Zheng Kou & Maryam Akhoundi & M. Ghassemi & A. A. Talebi & G. Muhiuddin, 2022. "Some Results in Neutrosophic Cubic Graphs with an Application in School’s Management System," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    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. Zheng Kou & Maryam Akhoundi & Xiang Chen & Saber Omidi, 2022. "A Study on Vague Graph Structures with an Application," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    6. Yanjiu Zhang & Shuxin Tian, 2025. "Grid-Connected Harmonic Suppression Strategy Considering Phase-Locked Loop Phase-Locking Error Under Asymmetrical Faults," Energies, MDPI, vol. 18(9), pages 1-24, April.
    7. Xiaolong Shi & Saeed Kosari & N. Mehdipoor & A.A. Talebi & G. Muhiuddin, 2022. "Novel Concepts in Vague Graphs with Application in Hospital’s Management System," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    8. 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).

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