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Fuzzy Domination and Independence: New Mathematical Insights and Bounds |
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PP: 629-641 |
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doi:10.18576/amis/200304
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Author(s) |
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Sulieman Shelash Mohammad,
Yogeesh Nijalingappa,
Hanan Jadallah,
Raja Natarajan,
Asokan Vasudevan,
Linga Raju,
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Abstract |
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| This paper investigates fuzzy domination and independence in fuzzy graphs, extending classical graph theory results to settings with uncertain or partial edge relationships. We introduce novel upper and lower bounds for the fuzzy domination number γ f and the fuzzy independence number α f , adapting well-known crisp graph inequalities (e.g., γ + α ≤ n) to accommodate edge membership degrees. Special attention is given to bipartite and planar fuzzy graphs, for which we derive refined, and sometimes exact, results. We also illustrate how concepts such as average fuzzy degree, minimum and maximum fuzzy degrees, and Euler-type formulas in planar embeddings guide the design of sharper bounds. To validate these theoretical findings, we provide constructed examples, including a bipartite uniform fuzzy graph and a planar fuzzy cycle, and show how total membership in fuzzy dominating or independent sets can be computed to match or closely approximate the new bounds. Finally, we discuss the implications of our results for real-world applications ranging from sensor coverage and social network analysis to transportation and bioinformatics, highlighting directions for future work in more advanced fuzzy graph contexts. |
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