Structure-based topological descriptors/indices of complex chemical networks enable prediction of physico-chemical properties and the bioactivities of these compounds through QSAR/QSPR methods. In this paper, we have developed a rigorous computational and theoretical technique to compute various distance-based topological indices of complex chemical networks. A fullerene is called the IPR (Isolated-Pentagon-Rule) fullerene, if every pentagon in it is surrounded by hexagons only. To ensure the applicability of our technique, we compute certain distance-based indices of an infinite family of IPR fullerenes. Our results show that the proposed technique is more diverse and bears less algorithmic and combinatorial complexity.