Computing two types of geometric-arithmetic indices of some benzenoid graphs

Document Type : Original Article

Authors

1 Department of Mathematics, Payame Noor University

2 Department of Mathematics, Yazd university

Abstract

The geometric-arithmetic index is a topological index was defined as $GA(G)=\sum{uv\in E(G)}\frac{2\sqrt{d_ud_v}}{d_u+d_v}}$, where du denotes the degree of vertex u in G. By replacing instead $\delta_u=\sum_{v\cong u} d_v$ of du in GA(G), we have a new version of this index that defined as $GA(G)=\sum{uv\in E(G)}\frac{2\sqrt{\delta_u\delta_v}}{\delta_u+\delta_v}}$. In this paper, we present exact formulas of these indices for some benzenoid graphs.

Graphical Abstract

Computing two types of geometric-arithmetic indices of some benzenoid graphs

Keywords

References

[1] A. R. Ashrafi and H. Shabani, GA index and Zagreb indices of nanocones, Optoelectron. Adv. Mater. Rapid Comm., 4(11)(2010) 1874-1876.
[2] G. H. Fath-Tabar, B. Furtula and I. Gutman, A new geometric-arithmetic index, J. Math. Chem., 47 (2010) 477-486.
[3] M. Ghorbani and A. Khaki, A note on the fourth version of geometric-arithmetic index, Optoelectron. Adv. Mater. Rapid Comm., 4 (2010) 2212-2215.
[4] A. Graovać, M. Ghorbani and M. A. Hosseinzadeh, Computing fifth geometric arithmetic index for nanostar dendrimers, Journal of Math-ematical Nanoscience, 1(2011) 33-42.
[5] A. Iranmanesh and M. Zeraatkar, Computing GA index for some nanotubes, Optoelectron. Adv. Mater. Rapid Comm., 4(11)(2010) 1852-1855.
[6] A. Khaksar, M. Ghorbani and H. R. Maimani, On atom bond connectivity and GA indices of nanocones, Optoelectron. Adv. Mater. Rapid Comm., 4(11)(2010) 1868-1870.
[7] M. Randić, On characterization of molecular branching. J. Am. Chem. Soc., 97 (1975) 6609-6615.
[8] H. Shabani and A. R. Ashrafi, Computing the GA index of nanotubes and nanotori, Optoelectron. Adv. Mater. Rapid Comm., 4(11)(2010) 1860-1862.
[9] R. Todeschini, V. Consonni, Handbook of Molecular Descriptors, Wileyn VCH, Weinheim, 2000.
[10] N. Trinajstić, Chemical Graph Theory, CRC Press, Boca Raton, FL, 1992.
[11] D.Vukičević and B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem., 46 (2009) 1369-1376.
[12] H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc., 69 (1947) 17-20.
[13] L. Xiao, S. Chen, Z. Guo and Q. Chen, The geometric-arithmetic index of Benzenoid Systems and Phenylenes, Int. J. Contemp. Math. Sciences. 5 (45) (2010) 2225-2230.
[14] B. Zhou, I. Gutman, B. Furtula and Z. Du, On two types of geometric arithmetic index, Chem. Phys. Lett., 482 (2009) 153-155.
Journal of Discrete Mathematics and Its Applications
Volume 8, Issue 3
September 2023

Files

History

  • Receive Date: 02 August 2014
  • Revise Date: 10 December 2014
  • Accept Date: 01 April 2015
  • Publish Date: 01 September 2023

Share

How to cite

Statistics