Delta Degree-Based Indices of Prime Coprime Graph for Integers Modulo Group

Research on prime coprime graphs of finite groups has largely focused on structural properties, spectra, and classical topological indices, with limited attention given to delta degree-based indices. To address this gap, this study investigates delta degree-based topological indices of the prime coprime graph constructed on the group of integers modulo n, Zn. In this graph, the vertices correspond to the elements of Zn, and two distinct vertices are adjacent if and only if the greatest common divisor of their orders is either 1 or a prime number. In the present work, the focus lies on computing and analyzing several delta degree-based topological indices that are obtained by incorporating the concept of delta degree into classical topological indices, including the delta first Zagreb index, the delta second Zagreb index, the delta hyper Zagreb index, and the delta forgotten index. The methodology involves deriving formulas for these delta-based indices for various values of n, supported by systematic computations and data tabulation. Beyond purely algebraic computation, statistical tools are employed to investigate the relationships between different indices. In particular, a comparative distribution analysis is conducted to determine whether pairs of indices exhibit similar patterns of variability using the Levene test.