A topological index is a mathematical formula that can be used to model any molecular structure on any graph. Topological indices are used to predict the physical, and bioactivity of corresponding chemical compounds. The symmetry of molecular structures is captured in topological indices, which give the structures a scientific terms to determine features like boiling temperatures, viscosity, and gyrating radius. Carbon allotropes in the form of nanostructures called carbon nanotubes have a cylindrical shape. An example of a fullerene is the carbon nanotube, which has uses in nanotechnology, electronics, optics, materials science, and architecture. We compute the First and Second Zagreb index, Hyper index, Zagreb Polynomial, and Augmented Zagreb index of H - Naphtalenic nanotubes.