Topological Invariants of Hexagonal Cage Network by Using Algebraic Polynomials

In this article, we go beyond earlier limits in the analysis by using algebraic polynomials to compute the topological indices for hexagonal cage networks. We investigate hexagonal cage networks of different orders and copies by introducing M-Polynomials and Forgotten polynomials, and we derive novel closed formulae and conclusions for a broad range of topological indices. We also create an efficient technique to compute , a pivotal polynomial, as part of our work. In addition to computing, we apply algebraic polynomials to the analysis of these indices, providing more insights into their structural significance in hexagonal cage networks. This work illuminates the algebraic underpinnings of these intricate networks and broadens the scope of topological index computation, with implications for a variety of scientific domains. These polynomials allow us to calculate several features of the network, such as the first and second Zagreb, modified Zagreb, General Randić, inverse General Randić, harmonic, symmetric division, inverse sum, and so on. There are now new closed formulae and outcomes available. Additionally, we offer a technique for calculating the polynomial . We also use algebraic polynomials to analyses all of the aforementioned indices.