On the great success of bond-additive topological indices such as Szeged, Padmakar-Ivan, Zagreb, and irregularity measures, yet another index, the Mostar index, has been introduced recently as a quantitative refinement of the distance nonbalancedness and also a peripherality measure in molecular graphs and networks. In this direction, we introduce other variants of bond-additive indices, such as edge-Mostar and total-Mostar indices. The present article explores a computational technique for Mostar, edge-Mostar, and total-Mostar indices with respect to the strength-weighted parameters. As an application, these techniques are applied to compute the three indices for the family of coronoid and carbon nanocone structures. © 2019 Wiley Periodicals, Inc.