Generalized -dependent polynomials of topological indices of the identity graph for the ring Z

In this article, we present the generalized rho dependent polynomials for the calculations of eccentricity, distance, total distance, and degree-based topological indices of the identity graph of Z rho. This is a thorough work in which we present many topological indices and co indices as rho dependent polynomials. The polynomials presented here can play a key role in the further development of the theory of topological indies for commutative rings. This paper presents a brand new approach to generalizing the topological indices because instead of the traditional way. A set-theoretic method is introduced here that can be very helpful and game-changing in the field of algebraic graph theory first of all sets of vertices for the identity graph of the commutative ring Z rho are partitioned into various sets, which makes it easier to generalize the degrees, distances, and eccentricities of this graph. This paper presents various results that make it easier to generalize the topological indices of the identity graph of Z rho.