## Abstract

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: ABC_{4}(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: GA_{5}(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 ABC_{4} and fifth geometric-arithmetic index GA_{5} and give close formulae of these indices for HAC_{5}C_{7}[p,q], HAC_{5}C_{6}C_{7}[p,q] and TUC_{4}C_{8}(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 language | English |
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Pages (from-to) | 70-76 |

Number of pages | 7 |

Journal | Journal of Computational and Theoretical Nanoscience |

Volume | 12 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2015 |

Externally published | Yes |

## Keywords

- 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

- Chemistry(all)
- Materials Science(all)
- Condensed Matter Physics
- Computational Mathematics
- Electrical and Electronic Engineering