Advertisement

Further Results on Two Families of Nanostructures

  • Zahra YarahmadiEmail author
  • Mircea V. Diudea
Chapter
Part of the Carbon Materials: Chemistry and Physics book series (CMCP, volume 9)

Abstract

A topological index is a numeric quantity derived from the structure of a graph which is invariant under automorphisms of the graph under consideration. In this chapter, the Wiener, Szeged, and Cluj-Ilmenau indices and one-alpha descriptor will be calculated for an infinite family of nanocones, CNC 4[n], and eccentric connectivity; augmented eccentric connectivity; and Wiener, Szeged, PI, vertex PI, and the first and second Zagreb indices of N-branched phenylacetylenes nanostar dendrimers will be obtained. For obtaining Wiener and Szeged indices, we use a powerful method given by Klavžar.

Keywords

Molecular Descriptor Mathematical Property Topological Index Connectivity Index Opposite Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Alipour MA, Ashrafi AR (2009a) A numerical method for computing the Wiener index of one-heptagonal carbon nanocone. J Comput Theor Nanosci 6:1204–1207CrossRefGoogle Scholar
  2. Alipour MA, Ashrafi AR (2009b) Computer calculation of the Wiener index of one-pentagonal carbon nanocone. Dig J Nanomater Biostruct 4:1–6Google Scholar
  3. Ashrafi AR, Mirzargar M (2008) PI, Szeged and edge Szeged indices of an infinite family of nanostar dendrimers. Indian J Chem 47A:538–541Google Scholar
  4. Ashrafi AR, Rezaei F (2007) PI index of polyhex nanotori. MATCH Commun Math Comput Chem 57:243–250Google Scholar
  5. Ashrafi AR, Ghorbani M, Jalali M (2008) The vertex PI and Szeged polynomials of an infinite family of fullerenes. J Theor Comput Chem 7:221–231CrossRefGoogle Scholar
  6. Ashrafi AR, Došlić T, Saheli M (2011) The eccentric connectivity index of TUC4C8(R) nanotubes. MATCH Commun Math Comput Chem 65:221–230Google Scholar
  7. Bharathi P, Patel U, Kawaguchi T, Pesak DJ, Moore JS (1995) Improvements in the synthesis of phenylacetylene monodendrons including a solid-phase convergent method. Macromolecules 28:5955–5963CrossRefGoogle Scholar
  8. Cameron PJ (1994) Combinatorics: topics, techniques, algorithms. Cambridge University Press, CambridgeGoogle Scholar
  9. Devillers J, Balaban AT (1999) Topological indices and related descriptors in QSAR and QSPR. Gordon and Breach, AmsterdamGoogle Scholar
  10. Diudea MV, Cigher S, John PE (2008) Omega and related counting polynomials. MATCH Commun Math Comput Chem 60:237–250Google Scholar
  11. Djoković D (1973) Distance preserving subgraphs of hypercubes. J Combin Theory Ser B 14:263–267CrossRefGoogle Scholar
  12. Dorosti N, Iranmanesh I, Diudea MV (2009) Computing the Cluj index of dendrimer nanostars. MATCH Commun Math Comput Chem 62:389–395Google Scholar
  13. Dureja H, Madan AK (2007) Superaugmented eccentric connectivity indices: new-generation highly discriminating topological descriptors for QSAR/QSPR modeling. Med Chem Res 16:331–341CrossRefGoogle Scholar
  14. Fischermann M, Homann A, Rautenbach D, Szekely LA, Volkmann L (2002) Wiener index versus maximum degree in trees. Discret Appl Math 122:127–137CrossRefGoogle Scholar
  15. Gupta S, Singh M, Madan AK (2002) Application of graph theory: relationship of eccentric connectivity index and Wiener’s index with anti-inflammatory activity. J Math Anal Appl 266:259–268CrossRefGoogle Scholar
  16. Gutman I (1994) A formula for the Wiener number of trees and its extension to graphs containing cycles. Graph Theory Notes N Y 27:9–15Google Scholar
  17. Gutman I, Das KC (2004) The first Zagreb index 30 years after. MATCH Commun Math Comput Chem 50:83–92Google Scholar
  18. Gutman I, Trinajstic N (1972) Graph theory and molecular orbitals, total π- electron energy of alternant hydrocarbons. Chem Phys Lett 17:535–538CrossRefGoogle Scholar
  19. Ilić A, Gutman I (2011) Eccentric connectivity index of chemical trees. MATCH Commun Math Comput Chem 65:731–744Google Scholar
  20. Iranamanesh I, Gholami NA (2009) Computing the Szeged index of Styrylbenzene dendrimer and Triarylamine dendrimer of generation 1–3. MATCH Commun Math Comput Chem 62:371–379Google Scholar
  21. John PE, Vizitiu AE, Cigher S, Diudea MV (2007) CI index in tubular nanostructures. MATCH Commun Math Comput Chem 57:479–484Google Scholar
  22. Karelson M (2000) Molecular descriptors in QSAR/QSPR. Wiley-Interscience, New YorkGoogle Scholar
  23. Khadikar PV (2000) Fabrication of indium bumps for hybrid infrared focal plane array applications. Natl Acad Sci Lett 23:113–118Google Scholar
  24. Khadikar PV, Karmarkar S (2001) A novel PI index and its applications to QSPR/QSAR studies. J Chem Inf Comput Sci 41:934–949CrossRefGoogle Scholar
  25. Khalifeh MH, Yousefi-Azari H, Ashrafi AR (2009) The first and second Zagreb indices of some graph operations. Discret Appl Math 157:804–811CrossRefGoogle Scholar
  26. Klavžar S (2006) On the canonical metric representation, average distance, and partial Hamming graphs. Eur J Comb 27:68–73CrossRefGoogle Scholar
  27. Klavžar S (2008) A bird’s eye view of the cut method and a survey of its applications in chemical graph theory. MATCH Commun Math Compu Chem 60:255–274Google Scholar
  28. Kumar V, Sardana S, Madan AK (2004) Predicting anti–HIV activity of 2,3–diary l–1,3–thiazolidin–4–ones:computational approaches using reformed eccentric connectivity index. J Mol Model 10:399–407CrossRefGoogle Scholar
  29. Mirzargar M (2009) PI, Szeged and edge Szeged polynomials of a dendrimer nanostar. MATCH Commun Math Comput Chem 62:363–370Google Scholar
  30. Sardana S, Madan AK (2001) Application of graph theory: relationship of molecular connectivity index, Wiener’s index and eccentric connectivity index with diuretic activity. MATCH Commun Math Comput Chem 43:85–98Google Scholar
  31. Sharma V, Goswami R, Madan AK (1997) Eccentric connectivity index: a novel highly discriminating topological descriptor for structure property and structure activity studies. J Chem Inf Comput Sci 37:273–282CrossRefGoogle Scholar
  32. Todeschini R, Consonni V (2000) Handbook of molecular descriptors. Wiley-VCH, WeinheimCrossRefGoogle Scholar
  33. Trinajstić N (1992) Chemical graph theory. CRC Press, Boca RatonGoogle Scholar
  34. Vukičević D, Bralo M, Klarić A, Markovina A, Spahija D, Tadić A, Žilić A (2010) One-two descriptor. J Math Chem 48:395–400CrossRefGoogle Scholar
  35. Wiener H (1947) Structural determination of paraffin boiling points. J Am Chem Soc 69:17–20CrossRefGoogle Scholar
  36. Winkler P (1984) Isometric embeddings in products of complete graphs. Discret Appl Math 7:221–225CrossRefGoogle Scholar
  37. Yarahmadi Z (2010) Eccentric connectivity and augmented eccentric connectivity indices of N-branched Phenylacetylenes nanostar dendrimers. Iranian J Math Chem 1(2):105–110Google Scholar
  38. Yarahmadi Z, Fath-Tabar GH (2011) The Wiener, Szeged, PI, vertex PI, the first and second Zagreb indices of N-branched Phenylacetylenes dendrimers. MATCH Commun Math Comput Chem 65:201–208Google Scholar
  39. Yousefi-Azari H, Ashrafi AR, Bahrami A, Yazdani J (2008) Computing topological indices of some types of benzenoid systems and nanostars. Asian J Chem 20:15–20Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesKhorramabad Branch, Islamic Azad UniversityKhorramabadIran
  2. 2.Department of Chemistry, Faculty of Chemistry and Chemical EngineeringBabes-Bolyai UniversityCluj-NapocaRomania

Personalised recommendations