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Application of Fuzzy Network Using Efficient Domination

Author

Listed:
  • Narayanan Kumaran

    (Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, India)

  • Annamalai Meenakshi

    (Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, India)

  • Miroslav Mahdal

    (Department of Control Systems and Instrumentation, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 17. Listopadu 2172/15, 708 00 Ostrava, Czech Republic)

  • Jayavelu Udaya Prakash

    (Department of Mechanical Engineering, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, India)

  • Radek Guras

    (Department of Control Systems and Instrumentation, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 17. Listopadu 2172/15, 708 00 Ostrava, Czech Republic)

Abstract

Let H eff ( V eff , E eff ) be a finite simple connected graph of order m with vertex set V eff and edge set E eff . A dominating set S d s ⊆ V e f f is called an efficiently dominating set if, for every vertex u a ∈ V G , N G u a ∩ S d s = 1 —where NG [ u a ] denotes the closed neighborhood of the vertex u a . Using efficient domination techniques and labelling, we constructed the fuzzy network. An algorithm has been framed to encrypt and decrypt the secret information present in the network, and furthermore, the algorithm has been given in pseudocode. The mathematical modelling of a strong fuzzy network is defined and constructed to elude the burgeoning intruder. Using the study of the efficient domination of fuzzy graphs, this domination parameter plays a nuanced role in encrypting and decrypting the framed network. One of the main purposes of fuzzy networks is encryption, so one of our contributions to this research is to build a novel combinatorial technique to encrypt and decode the built-in fuzzy network with a secret number utilizing effective domination. An illustration with an appropriate secret message is provided along with the encryption and decryption algorithms. Furthermore, we continued this study in intuitionistic fuzzy networks.

Suggested Citation

  • Narayanan Kumaran & Annamalai Meenakshi & Miroslav Mahdal & Jayavelu Udaya Prakash & Radek Guras, 2023. "Application of Fuzzy Network Using Efficient Domination," Mathematics, MDPI, vol. 11(10), pages 1-20, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2258-:d:1144822
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    References listed on IDEAS

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    1. Enrico Enriquez & Grace Estrada & Carmelita Loquias & Reuella J Bacalso & Lanndon Ocampo, 2021. "Domination in Fuzzy Directed Graphs," Mathematics, MDPI, vol. 9(17), pages 1-14, September.
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    Cited by:

    1. Annamalai Meenakshi & Adhimoolam Kannan & Robert Cep & Muniyandy Elangovan, 2023. "Efficient Graph Network Using Total Magic Labeling and Its Applications," Mathematics, MDPI, vol. 11(19), pages 1-21, September.
    2. Annamalai Meenakshi & Adhimoolam Kannan & Miroslav Mahdal & Krishnasamy Karthik & Radek Guras, 2023. "A Comparative Study of Fuzzy Domination and Fuzzy Coloring in an Optimal Approach," Mathematics, MDPI, vol. 11(18), pages 1-16, September.

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