Computing the theta polynomial Θ(G,x) and the theta index Θ(G) of titania nanotubes TiO2(m,n)

Yingfang Li, Li Yan, Mohammad R. Farahani, Muhammad Imran, Muhammad K. Jamil

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Let G = (V ,E) be a simple connected molecular graph in chemical graph theory, where the vertex/ atom set and edge/bond set of G denoted by V (G) and E(G), respectively and its vertices correspond to the atoms and the edges correspond to the bonds. Two counting polynomials the "Omega Ω(G,x) and Theta Θ(G,x)" polynomials of a molecular graph G were defined by Diudea as Θ(G,x) =Σe∈E(G) xn(e) and Θ(G,x) = Σe∈E(G) n(e)xn(e) where n(e) denotes the number of edges co-distant with the edge e. From definition of these counting polynomials, we can obtain the Theta polynomial by inserting the coefficient n(e) in the Omega polynomial. Then the Theta index will be the first derivative of the Theta polynomial Θ(G,x) evaluated at x = 1. The goal of this paper is to compute the Theta polynomial Θ(G,x) and the Theta index Θ(G) of an infinite family of the Titania Nanotubes TiO2(m,n) for the first time.

Original languageEnglish
Pages (from-to)715-717
Number of pages3
JournalJournal of Computational and Theoretical Nanoscience
Volume14
Issue number1
DOIs
Publication statusPublished - Jan 2017

Keywords

  • Co-distant
  • Molecular graph
  • Omega polynomial
  • Qoc strip
  • Theta polynomial
  • Titania nanotubes TiO(m,n)

ASJC Scopus subject areas

  • General Chemistry
  • General Materials Science
  • Condensed Matter Physics
  • Computational Mathematics
  • Electrical and Electronic Engineering

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