Topological indices of the subdivision of a family of partial cubes and computation of SiO2 related structures

The aim of this paper is to apply the Djokovi-Winkler relation to subdivisions of partial cubes and then to derive closed formulae for computing the topological indices of the subdivision graphs, provided the indices of its associated partial cubes are known. We have applied the obtained formulae to the subdivisions of circumcoronenes to compute the exact analytical expressions of its distance and degree-distance based indices. We have also obtained distance-based and degree-distance based indices of silicate graphs such as pruned quartz. Such silicate molecular structures have potential applications in nanomedicine for drug delivery systems, as these materials could serve as molecular belts for efficient drug delivery.