Fuzzy graphs have many applications not only in mathematics but also in any field of science where the concept of fuzziness is involved. The notion of fuzziness is suitable in any environment, which favor to predicts the problem and solve this problem in a decent way. As compared to crisp theory, fuzzy graphs are a more beneficial and powerful tool to get better accuracy and precision due to their fuzziness property. A topological index is a numerical value which characterizes the properties of the graph. Topological indices were basically developed for chemical structures, but these are also used for general graphs as well. In chemical graph theory, topological indices are used to extract the chemical properties of the graphs. These indices are also well studied in fuzzy environment. Applications of fuzzy graphs are found in medicines, telecommunications, traffic light control, and many more. Our aim is to find these fuzzy topological indices for flower graphs to strengthen the concepts of fuzziness in general graphs. In this paper, some novel results for fm×r flower graphs are achieved.