Journal of Mathematical Chemistry

, Volume 57, Issue 1, pp 343–369 | Cite as

Distance-based topological indices of nanosheets, nanotubes and nanotori of \(\hbox {SiO}_2\)

  • Micheal Arockiaraj
  • Sandi Klavžar
  • Shagufa MushtaqEmail author
  • Krishnan Balasubramanian
Original Paper


We have computed distance-based topological indices of nanosheets, nanotubes and nanotori of \(\hbox {SiO}_2\) which find potential applications in drug, food, and cosmetic industry. As topological indices correlate with physico-chemical properties and estimating efficiency of drug deliveries of these species, we compute the topological indices based on their degrees and distances of the associated molecular graphs. We have obtained exact analytical expressions of various topological indices such as the Wiener, vertex-Szeged, edge-Szeged, edge-vertex-Szeged, Padmakar-Ivan, Schultz and Gutman indices of \(\hbox {SiO}_2\) nanosheet, nanotube and torus using the cut method which involves decomposing a molecular graph by means of the transitive closure property of Djoković–Winkler relation to smaller strength-weighted quotient graphs.


Silicon dioxide nanostructures Drug delivery QSAR/QSPR Cut method Topological indices 


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsLoyola CollegeChennaiIndia
  2. 2.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia
  3. 3.Faculty of Natural Sciences and MathematicsUniversity of MariborMariborSlovenia
  4. 4.Institute of Mathematics, Physics and MechanicsLjubljanaSlovenia
  5. 5.School of Molecular SciencesArizona State UniversityTempeUSA

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