Enhancing Security in Fuzzy Networks Through Efficient Domination

Let G(V, E) be a finite simple connected graph of order m with vertex set V and edge set E. A dominating set S ⊆ V(G) is called an efficiently dominating set if, for every vertex u ∈ V(G), N[u] ∩ S = 1, where N[u] denotes the closed neighborhood of the vertex. Using efficient domination techniques and labeling, we constructed the different types of fuzzy networks. An algorithm has been framed to encrypt and decrypt the secret information present in the network. The mathematical modeling of a strong type of fuzzy network is defined and constructed to elude the burgeoning intruder. Using the study of efficient domination on types of fuzzy graphs, this domination parameter plays a nuanced role in encrypting and decrypting the framed network. The main purpose of types of fuzzy network are encryption and decryption, our contributions to this research is to build a novel combinatorial technique to encrypt and decrypt 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.