In this study we consider relatively new bond-additive Mostar indices that appear to provide quantitative measures of peripheral shapes of molecules. We have computed weighted Mostar, edge-Mostar and total-Mostar indices of graphene, α-types of graphyne and graphdiyne, which are of considerable interest owing to their novel properties and thus find applications in a number of areas such as sensors, catalysis, chemisorption and nanomedicine. We have implemented the results to analyse the weighted Mostar indices and have obtained exact analytical expressions for the title molecules. We propose that Mostar indices together with frontier molecular orbitals, and HOMO–LUMO gaps can provide measures of chemical reactivity and analysis of peripheral molecular shapes. © 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group.