Journal of Modern Technology and Engineering

Graph theory is an indispensable mathematical tool for both predicting chemical molecular modeling and determining chemical properties, as well as analyzing the resilience of complex networks. This study focuses on the computational analysis of topological indices, which play a critical role in predicting the physicochemical properties of compounds and determining the structural robustness of network topologies. The literature contains many methods for calculating topological index values, such as degree-based, distance-based, and others. Recently, reverse degree-based topological indices have been defined. This study considers Mycielski graphs, which are constructed on top of cycle graphs, one of the fundamental graph structures. Closed form formulas have been obtained for twelve different reverse degree-based topological indices for these graphs. Furthermore, the computational results are explained and supported by detailed numerical data. The obtained mathematical expressions quantitatively demonstrate the relationship between structural stability and topological connectivity. These theoretical findings provide a comprehensive basis for evaluating the connectivity properties of both chemical structures and technological networks.