Abstract
Fuzzy graphs and fuzzy labelings are crucial in modeling real-time systems by accommodating varying degrees of information precision. In this paper, we introduce a novel fuzzy labeling called Elegant Fuzzy Labeling. We prove that a simple graph admits Elegant Fuzzy Labeling if and only if it admits elegant labeling. Furthermore, we prove that while a simple graph that admits Elegant Fuzzy Labeling also admits fuzzy labeling, but not conversely. We identify specific classes of simple graphs that admit Elegant Fuzzy Labeling and explore practical application of this new labeling approach.
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