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A Comparative Study of Fuzzy Domination and Fuzzy Coloring in an Optimal Approach

Author

Listed:
  • Annamalai Meenakshi

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

  • Adhimoolam Kannan

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

  • Miroslav Mahdal

    (Department of Control Systems and Instrumentation, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 17. Listopadu 2172/15, 70800 Ostrava, Czech Republic)

  • Krishnasamy Karthik

    (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, 70800 Ostrava, Czech Republic)

Abstract

An optimal network refers to a computer or communication network designed, configured, and managed to maximize efficiency, performance, and effectiveness while minimizing cost and resource utilization. In a network design and management context, optimal typically implies achieving the best possible outcomes between various factors. This research investigated the use of fuzzy graph edge coloring for various fuzzy graph operations, and it focused on the efficacy and efficiency of the fuzzy network product using the minimal spanning tree and the chromatic index of the fuzzy network product. As a network made of nodes and vertices, measurement with vertices is a parameter for domination, and edge measurement is a parameter for edge coloring, so we used these two parameters in the algorithm. This paper aims to identify an optimal network that can be established using product outcomes. This study shows a way to find an optimal fuzzy network based on comparative optimal parameter domination and edge coloring, which can be elaborated with applications. An algorithm was generated using an optimal approach, which was subsequently implemented in the form of applications.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:4019-:d:1245066
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    References listed on IDEAS

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    1. 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.
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