Abstract

Graph labeling under various constraints is crucial for modeling complex systems, allowing different levels of information precision. Elegant Fuzzy Labeling, a flexible fuzzy labeling model, enhances adaptability over traditional methods. It accommodates diverse labeling approaches for different translation constants, broadening its applicability. In this paper, we extend Elegant Fuzzy Labeling to star graphs and their variants. We prove that all star graphs and the join of two star graphs admit this labeling. Additionally, we establish conditions for bistar graphs to admit this labeling, paving the way for further research in this domain.