The Omega and Sadhana polynomials of TUC₄[ p, q ] nanotubes

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 TUC₄[p,q] and provide its mathematical proof. We also give explicit formulae for the PI and the theta polynomial of TUC₄[p,q] nanotubes.