On the Study Sum Graph of the Group Z_(βγρ) with Some Topological Indices

In this study, we examine the application of graph theory to the sum group with Z_βγρ, where β,γ and ρ are a prime numbers. We explore the idea of two distinguished orders, where the sum is permanent greatest and equivalent to the order of the group Z_βγρ. We demonstrate that the group sum graph of Z_βγρ is linked and cyclic, among other properties, when certain conditions of graph theory are satisfied. Additionally, we determine all the degrees of the graphs and calculate some the well-known topological indices by generalizing them.