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The edge version of geometric arithmetic index of nanotubes and nanotori

MOHAMAD NAZRI HUSIN1, ROSLAN HASNI1,* , MUHAMAD IMRAN2, HAILIZA KAMARULHAILI3

Affiliation

  1. School of Informatics and Applied Mathematics, University Malaysia Terengganu, 21030 Kuala Terengganu, Terengganu, Malaysia
  2. Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, Sector H-12, Islamabad, Pakistan
  3. School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Penang, Malaysia

Abstract

The edge version of geometric arithmetic index of graph 𝐺, abbreviated as 𝐺𝐴𝑒(𝐺), is defined as 𝐺𝐴𝑒(𝐺)=Ξ£2βˆšπ‘‘πΏ(𝐺)(𝑒)𝑑𝐿(𝐺)(𝑓)𝑑𝐿(𝐺)(𝑒)+ 𝑑𝐿(𝐺)(𝑓)π‘’π‘“βˆˆπΈ(𝐿(𝐺), where 𝑑𝐿(𝐺)(𝑒) denotes the degrees of an edge 𝑒 of line graph of G. In this paper, the closed formulas for 𝐺𝐴𝑒 index for some nanotubes and nanotorus are given..

Keywords

Geometric arithmetic index, Nanotubes, Nanotorus.

Citation

MOHAMAD NAZRI HUSIN, ROSLAN HASNI, MUHAMAD IMRAN, HAILIZA KAMARULHAILI, The edge version of geometric arithmetic index of nanotubes and nanotori, Optoelectronics and Advanced Materials - Rapid Communications, 9, 9-10, September-October 2015, pp.1292-1300 (2015).

Submitted at: July 8, 2015

Accepted at: Sept. 9, 2015