Computing fifth geometric-arithmetic index for nanostar dendrimers

Document Type : Full Length Article

Authors

1 Institute R. Bošković, HR-10002 Zagreb, POB 180, Croatia, and Faculty of Science, University of Split Nikole Tesle 12, HR-21000, Split, Croatia

2 Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785 – 136, I. R. Iran

Abstract

The geometric-arithmetic index is a topological index was defined as GA(G)=∑uv2(dudv)1/2/(du+dv), in which degree of vertex u denoted by dG(u ). Now we define a new version of GA index as GA5(G)=∑uv2(δuδv)1/2/(δuv) ,  where δu=∑uvdv. The goal of this paper is to further the study of the GA5 index.

Graphical Abstract

Computing fifth geometric-arithmetic index for nanostar dendrimers

Keywords


REFERENCES
1. H. Wiener, Structural determination of paraffin boiling points, J. Amer. Chem. Soc.,69 (1947), 17-20.
2. B. Furtula, A. Graovac and D. Vukičević, Atom–bond connectivity index of trees, Disc. Appl. Math., 157 (2009), 2828 - 2835.
3. D. Vukičević and B. Furtula, Topological index based on the ratios ofgeometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem., 46 (2009), 1369 − 1376.
4. GH. Fath-Tabar, B. Furtula and I. Gutman, A new geometric--arithmetic index, J. Math. Chem., 47 (2010), 477 – 486.
5. B. Zhou, I. Gutman, B. Furtula and Z. Du, On two types of geometric-arithmetic index, Chem. Phys. Lett., 482  (2009), 153 – 155.
6. M. Ghorbani and A. Khaki, A note on the fourth version of geometric-arithmetic index, Optoelectron. Adv. Mater. – Rapid Comm., 4(12) (2010), 2212-2215.
7. N. Trinajstić and I. Gutman, Mathematical Chemistry, Croat. Chem. Acta, 75 (2002), 329 – 356.
8. A. R. Ashrafi, M. Ghorbani and M. Jalali, Computing Sadhana polynomial of V- phenylenic nanotubes and nanotori, Indian J. Chem., 47 (2008), 535 – 537.
9. A. R. Ashrafi and M. Ghorbani, PI and Omega polynomials of IPR fullerenes, Fullerenes, Nanotubes and Carbon Nanostructures, 18(3) (2010), 198 – 206.
10. A. R. Ashrafi, M. Ghorbani and M. Jalali, Study of IPR fullerenes by counting polynomials, Journal of Theoretical and Computational Chemistry, 8(3) (2009),451 – 457.
11. A. R. Ashrafi, M. Saheli and M. Ghorbani, The eccentric connectivity index of nanotubes and nanotori, Journal of Computational and Applied Mathematics, 235(16) (2011), 4561-4566.
12. The GAP Team: GAP, Groups, Algorithms and Programming, RWTH, Aachen, 1995.
13. A. R. Ashrafii and M. Ghorbani, Eccentric Connectivity Index of Fullerenes, 2008, In: I. Gutman, B. Furtula, Novel Molecular Structure Descriptors – Theory and Applications II, pp. 183 – 192.
Volume 1, 1-2
June 2011
Pages 33-42
  • Receive Date: 03 January 2011
  • Revise Date: 07 February 2011
  • Accept Date: 21 March 2011
  • Publish Date: 01 June 2011