1. The Omega and Sadhana polynomials of TU[C.sub.4][p,q] nanotubes
- Author
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Ahmad, Sarfraz, Ahmad, Uzma, Imran, Muhammad, and Farah, Nighat
- Subjects
Chemical research ,Polynomials -- Usage ,Nanotubes -- Research ,Chemistry - Abstract
The counting polynomials are useful in topological description of benzenoid structures. The quasi-orthogonal cut strips could account for the helicity of nanotubes and nanotori. It also helps to describe its topological indices by virtue of quasi-orthogonal cuts of the edge strips in the polycyclic graphs. In this article, we give a complete description of the Omega and Sadhana polynomials of the nanotube TU[C.sub.4][p,q] and provide its mathematical proof. We also give explicit formulae for the PI and the theta polynomial of TU[C.sub.4][p,q] nanotubes. Key words: Omega polynomial, Sadhana polynomial, TU[C.sub.4][p,q] nanotube. Les fonctions polynomiales de comptage sont utiles pour la description topologique des structures benzenoides. Les bandes de coupes quasi-orthogonales pourraient expliquer l'helicite des nanotubes et des nanotori. Elles pourraient egalement contribuer a la description de leurs indices topologiques grace aux coupes quasi-orthogonales des bandes d'aretes de graphes polycycliques. Dans le present article, nous presentons une description complete des fonctions polynomiales Omega et de Sadhana du nanotube TU[C.sub.4][p,q] et en faisons la demonstration mathematique. Nous presentons egalement les formules explicites des fonctions polynomiales PI et theta des nanotubes TU[C.sub.4][p,q]. [Traduit par la Redaction] Mots-cles: fonction polynomiale Omega, fonction polynomiale de Sadhana, nanotube TU[C.sub.4][p,q]., Introduction One of the remarkable achievements in the field of nanotechnology is carbon nanotube (CNT) synthesis. It was discovered by Iijima in 1991 (1). Two years later, two groups independently [...]
- Published
- 2016
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