In this paper, we give topological properties of collection of prime ideals in 2-primal near-rings. We show that Spec(N), the spectrum of prime ideals, is a compact space, and Max(N), the maximal ideals of N, forms a compact $T_1$-subspace. We also study the zero-divisor graph $Gamma_I$(R) with respect to the completely semiprime ideal I of N. We show that ${Gamma}_{mathbb{P}}$ (R), where $mathbb{P}$ is a prime radical of N, is a connected graph with diameter less than or equal to 3. We characterize all cycles in the graph ${Gamma}_{mathbb{P}}$ (R).