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Computing Omega, Sadhana and PI polynomials of benzoid carbon nanotubes

A. Q. BAIG1,* , MUHAMMAD IMRAN2, HAIDAR ALI1

Affiliation

  1. Department of Mathematics,COMSATS Institute of Information Technology, Attock, Pakistan
  2. Department of Mathematics,School of Natural Sciences (SNS),National University of Sciences and Technology (NUST), Sector H-12, Islamabad, Pakistan

Abstract

Counting polynomials are those polynomials having at exponent the extent of a property partition and coefficients the multiplicity/occurrence of the corresponding partition. These polynomials were proposed on the ground of quasi-orthogonal cuts edge strips in polycyclic graphs. These counting polynomials are useful in the topological description of bipartite structures as well as in counting some single number descriptors, i.e. topological indices. These polynomials count equidistant and non-equidistant edges in graphs.In this paper, Omega, Sadhana and PI polynomials are computed for Benzoid nanotubes for the first time. The analytical closed formulas of these polynomials for the circumcoronene series of benzenoid k H , hexagonal parallelogram P(m,n) and zigzag-edge coronoid fused with starphnene ZCS(k, l,m) nanotubes are derived in this paper..

Keywords

Counting polynomial, Omega polynomial, Sadhana polynomial, PI polynomial, k H nanotube, P(m,n) nanotube, ZCS(k, l,m) nanotube.

Citation

A. Q. BAIG, MUHAMMAD IMRAN, HAIDAR ALI, Computing Omega, Sadhana and PI polynomials of benzoid carbon nanotubes, Optoelectronics and Advanced Materials - Rapid Communications, 9, 1-2, January-February 2015, pp.248-255 (2015).

Submitted at: Oct. 22, 2014

Accepted at: Jan. 21, 2015