(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we study the zero-divisor graph of \( Z_[x]/x^5 \) for prime number \( \), denoted as \(Γ(Z_[x]/x^5 ) \), including its energy and topological indices. Specifically, we provide bounds of the energy for \(Γ(Z_[x]/x^5 ) \) and show that these bounds are numerically close to the actual energy value. Furthermore, we determine the topological indices of \(Γ(Z_[x]/x^5 ) \), including the topological indices based on distance and degree. We also perform numerical simulations of the topological indices for various prime numbers \( \).