Computation of certain topological indices of nanotubes

Sakander Hayat, Muhammad Imran

Research output: Contribution to journalArticlepeer-review

55 Citations (Scopus)


Among topological connectivity indices, the atom-bond connectivity (ABC) index and geometric-arithmetic (GA) index are of vital importance. The ABC index is defined as: ABC(G) = Σ uvεE(G) √ (dG(u)+dG(v)-2)/(dG(u)dG(v)), while GA(G) index also defined as follows: GA(G) = Σ uvεE(G)((2 √ dG(u)dG(v))/(dG(u)+dG(v))), where dG(u) denotes the degree of vertex u ε V (G). Recently, the fourth version of ABC index is proposed by Ghorbani et al. defined as follows: ABC4(G) = Σ uvεE(G) √ (δG(u)+δG(v)-2)/(δG(u)δG(v)). The fifth version of GA index is introduced by Graovac et al. defined as follows: GA5(G) = Σ uvεE(G)((2 √ δG(u)δG(v))/(δG(u)+δG(v))), where δu = Σ uvεE(G) dG(v). In this paper, we study the fourth atom-bond connectivity index ABC4 and fifth geometric-arithmetic index GA5 and give close formulae of these indices for HAC5C7[p,q], HAC5C6C7[p,q] and TUC4C8(R)[p,q] nanotubes and their corresponding nanotori. We also give a characterization of k-regular graphs with respect to their fifth geometric-arithmetic index.

Original languageEnglish
Pages (from-to)70-76
Number of pages7
JournalJournal of Computational and Theoretical Nanoscience
Issue number1
Publication statusPublished - Jan 1 2015
Externally publishedYes


  • ABC index
  • Atom-bond connectivity index
  • GA index
  • Geometric-arithmetic index
  • HACCC[p,q] nanotube
  • HACC[p,q] nanotube
  • Nanotorus
  • TUCC(R)[p,q] nanotube

ASJC Scopus subject areas

  • General Chemistry
  • General Materials Science
  • Condensed Matter Physics
  • Computational Mathematics
  • Electrical and Electronic Engineering


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