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

Annamalai Meenakshi, Adhimoolam Kannan, Miroslav Mahdal, Krishnasamy Karthik () and Radek Guras
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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
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

Mathematics, 2023, vol. 11, issue 18, 1-16

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.

Keywords: fuzzy coloring; minimum spanning tree; domination number; optimal network (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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