Efficient Network Modeling With Modular Multiplicative Divisor Labeling in Even Tentacled Jellyfish Graphs

Graph labeling plays a crucial role in network design, cryptography, and combinatorial optimization by structuring data representation for efficient processing. Modular Multiplicative Divisor (MMD) labeling is explored for Jellyfish graphs <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$J F(\eta, \theta)$</tex> with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\eta$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\theta$</tex> even tentacles, establishing a systematic labeling function that satisfies MMD conditions. The labeling ensures that the sum of all edge labels remains congruent to zero modulo a given integer, maintaining a structured and balanced distribution. Mathematical proofs and computational validation confirm the feasibility of MMD labeling in Jellyfish graphs. A comparative analysis with oddeven sum labeling and other existing techniques highlights its advantages in structured network modeling. The results contribute to advancing graph based computational models and provide insights into the structured application of modular arithmetic in labeling methodologies.