M-Polynomials and Degree-Based Topological Indices of VC5C7[p,q] and HC5C7[p,q] Nanotubes

Analysts are creating materials, for example, a carbon nanotube-based composite created by NASA that bends when a voltage is connected. Applications incorporate the use of an electrical voltage to change the shape (transform) of airship wings and different structures. Topological indices are numerical parameters of a molecular graph which characterize its topology and are usually graph invariant. Topological indices are used, for example, in the development of quantitative structure-activity relationships (QSARs) in which the biological activity or other properties of molecules are correlated with their chemical structure. Topological indices catch symmetry of molecular structures and help us to predict properties, for example, boiling points, viscosity, and the radius of gyrations of nanotubes. In this paper, we compute <inline-formula> <tex-math notation="LaTeX">${M}$ </tex-math></inline-formula>-polynomials of two nanotubes, <inline-formula> <tex-math notation="LaTeX">$VC_{5} C_{7} [p,q]$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$HC_{5} C_{7} [p,q]$ </tex-math></inline-formula>. By applying calculus on these <inline-formula> <tex-math notation="LaTeX">${M}$ </tex-math></inline-formula>-polynomials, we produce formulas of numerous degree-based topological indices, which are functions relying on parameters of the structure and, in combination, decide properties of the concerned polymeric compound.