Fuzzy Lucky Labeling and Proper Fuzzy Lucky Labeling of Special Graphs

Abstract—This paper introduces fuzzy lucky labelling and proper fuzzy lucky labeling of graphs. A fuzzy lucky labeling assigns fuzzy values from (0, 1] to vertices such that induced sums at adjacent vertices differ, while the proper version additionally requires distinct labels for neighbours. We establish key theorems, including existence results and relationships with chromatic number, and compute fuzzy lucky numbers for special graphs such as stars, bull graphs, and fork graphs.