Investigating Fuzzy Topological indices of Linear and Cyclic Anthracene Hydrocarbon

This research focuses on the theoretical examination of the fuzzy graph of aromatic hydrocarbon of Anthracene and computes several fuzzy-based degree topological indices. The research introduces new definitions for the first Zagreb fuzzy index, forgotten index, and Y−index, and provides a general formula for fuzzy topology indices of Anthracene hydrocarbon by considering the degree of each edge. Moreover, a general formula is presented to determine the specific topology index of a hydrocarbon-based on the number of rows and columns. We compared the topological indices of linear Anthracene and found that the Randic and harmonic indices had the highest values. Continuing with the drawing of the Randic index surface, we concluded that when the number of parameters in the rows and columns of the Anthracene hydrocarbon is equal, the Randic index has the highest value. This approach can help researchers predict and estimate compounds' physical and chemical properties using topology indices and precise bond lengths and atomic mass calculations through software.