IJPAM: Volume 116, No. 3 (2017)

Title

COMPUTATIONS OF CERTAIN TOPOLOGICAL INDICES
OF TITANIA NANOTUBES TiO$_{2}(m,n)$

Authors

Zeinab Foruzanfar$^1$, Mohammad Reza Farahani$^2$, Muhammad Kamran Jamil$^3$,
Hafiz Mutee ur Rehman$^4$, Muhammad Imran$^5$
$^1$Department of Engineering Sciences and Physics
Buein Zahra Technical University
Buein Zahra, Qazvin, IRAN
$^2$Department of Applied Mathematics
Iran University of Science and Technology (IUST)
Narmak, Tehran 16844, IRAN
$^3$Department of Mathematics
Riphah Institute of Computing and Applied Sciences (RICAS)
Riphah International University
14 Ali Road, Lahore, PAKISTAN
$^4$Department of Mathematics $\&$ Statistics
The University of Lahore
Lahore, PAKISTAN
$^5$Department of Mathematical Sciences
United Arab Emirates University
P.O. Box 15551, Al Ain, UNITED ARAB EMIRATES
$^5$Department of Mathematics
School of Natural Sciences (SNS)
National University of Sciences and Technology (NUST)
Sector H-12, Islamabad, PAKISTAN

Abstract

A topological index is a numeric quantity associated with a graph which characterizes the topology of graph and is invariant under graph automorphism. The third geometric-arithmetic index (GA${}_{3}$) of a graph G is defined as
$GA_{3}(G)=\sum\limits_{e=uv\in E(G)}\frac{2\sqrt{m_{v}.m_{u}}}{m_{v}+m_{u}}$. In this paper, we compute the third version of geometric-arithmetic index of the Titania Nanotubes $TiO_{2}(m,n)$.

History

Received: 2017-07-22
Revised: 2017-09-23
Published: October 26, 2017

AMS Classification, Key Words

AMS Subject Classification: 05C90, 05C35, 05C12
Key Words and Phrases: molecular graph, titania carbon nanotubes $TiO_{2}(m,n)$, orthogonal cuts, geometric-arithmetic index

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How to Cite?

DOI: 10.12732/ijpam.v116i3.22 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 116
Issue: 3
Pages: 765 - 776


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