| Summary: | Let <i>H<sub>eff</sub></i> (<i>V<sub>eff</sub></i>, <i>E<sub>eff</sub></i>) be a finite simple connected graph of order m with vertex set <i>V<sub>eff</sub></i> and edge set <i>E<sub>eff</sub></i>. A dominating set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>S</mi><mrow><mi>d</mi><mi>s</mi></mrow></msub><mo>⊆</mo><msub><mi>V</mi><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow></msub></mrow></semantics></math></inline-formula> is called an efficiently dominating set if, for every vertex <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>∈</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>,</mo><mo> </mo><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mfenced open="[" close="]" separators="|"><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>a</mi></mrow></msub></mrow></mfenced><mo>∩</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>d</mi><mi>s</mi></mrow></msub></mrow></mfenced><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>—where <i>NG</i> [<i>u<sub>a</sub></i>] denotes the closed neighborhood of the vertex <i>u<sub>a</sub></i>. 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.
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