In computational chemistry, the characteristics of a molecular compound can be evaluated with the help of a numerical value, known as a topological index. Topological indices are extensively used to study the molecular mechanics in QSAR and QSPR analysis. In this study, we introduced the vicinal degree and vicinal degree-based topological indices such as geometric-arithmetic vicinal index, atom bond connectivity vicinal index, harmonic vicinal index, inverse sum indeg vicinal index, Randic vicinal index, and sum-connectivity vicinal index for planar polyhex zigzag carbon nanotubes, where these carbon nanotubes (CNTs) are nanomaterials with broad applications that are produced on a large scale. Furthermore, we verify the correlation between the general degree-based topological indices and the vicinal degree-based topological indices, and the R code for finding these vicinal topological indices.