Group Theoretic Approach towards the Balaban Index of Catacondensed Benzenoid Systems and Linear Chain of Anthracene

In this work, we present the analytical closed forms of the Balaban index for anthracene and catacondensed benzenoid systems using group theoretic techniques. The Balaban index is a distance-based topological index that provides valuable information about the properties of chemical structures. We emphasize the importance of determining analytical closed forms of the Balaban index for catacondensed benzenoid systems and linear chains of anthracene, as it enables a deeper understanding of these systems and their behavior. Our analysis utilizes the group action of the automorphism group of these chains on the set of vertices, which refer to the points where the chains intersect. In future work, we plan to determine the Balaban index of other polymeric linear chains using group theoretic techniques and extend the applications of this index to other fields, such as materials science and biology. It is clear that the Balaban index remains a valuable tool in theoretical and computational chemistry, and its applications are constantly evolving.