On the normal product and modular product of product fuzzy graphs with applications to defense communication networks - Fery Firmansah; Niken Retnowati; Tasari (FoundAE, 2026)
Background: This study focuses on the development of new operations of product fuzzy graphs, specifically the normal product and modular product operations. The normal product of product fuzzy graphs is used to build infrastructure with maximum path redundancy. Meanwhile, the modular product operation of product fuzzy graphs is implemented to optimize the alignment of operational processes and information security. Aims: This study aims to define the normal product and modular product of product fuzzy graphs, define the properties of the normal product and modular product of product fuzzy graphs, and to apply to defense communication networks. Method: The research stages consist of formulating the definition of the normal product and modular product of product fuzzy graphs along with its properties and applying to defense communication networks. Results: The results of the study show that the normal product and modular product of product fuzzy graph is fuzzy graph, the normal product and modular product of strong product fuzzy graph is strong, consequently, the normal product and modular product of complete product fuzzy graph is strong. Conclusion: The application of the normal product and modular product of product fuzzy graph can produce a more compact defense communication network.