Improved Methods for Determining the Topological Indices of [n] Circulenes from the Central Polygonal Area

Abstract

Many researchers in computational and theoretical chemistry are fascinated by the structures of circlenes, which are
unusual cyclic compounds generated by alternating polygonal bonds. Their geometric and topological features are
particularly noteworthy. Numerous domains, such as materials science, nanochemistry, and medicines, make use of
these structures. For [n] circulenes, new formulae for distance-based topological indices are given in this study. By doing
away with the need for edge partitioning, these formulae hope to streamline and quicken the computation process. If
one knows the size of the center polygon in the circulon structure, they may simply compute the index using the general
formulae supplied for the Szeged, Mostar, and PI indices. There is a graphical comparison of several topological indices
and numerical findings are also provided. Additionally, we investigate the possible relationship between these indices
and certain physicochemical features of [n] circulenes. Along with the indexes' maximum and minimum values, we also
provide the index that, relative to the others, has the strongest link to the physicochemical attributes. These results are
helpful for future research since they do not need polynomials to be calculated.