Topological Characterization of the Full k-Subdivision of a Family of Partial Cubes and Their Applications to α-Types of Novel Graphyne and Graphdiyne Materials

Graphene, an allotrope of carbon, has gained tremendous importance due to its novel, chemical, structural, optical and reactivity properties. A class of graphene allotropes with both and sp carbons named alpha-types of graphyne and graphdiyne have been synthesized recently and have received considerable attention due to their novel structural and optical properties with multiple wide ranging applications in developing sensors, catalysis, chemisorption and nanomedicine. In the present study we have considered mathematical techniques for the topological characterization of these novel materials. We have extended full subdivisions of partial cubes in which transitive closure of Djokovic-Winkler relation is used to compute analytical expressions for various distance-based topological indices for their deployment in chemical and medicinal applications via QSAR and QSPR studies.