Exploring the properties of the zero-divisor graph of direct product of $*$-rings - Mohd Nazim; Nadeem Ur Rehman; Shabir Ahmad Mir (Journal of Mahani Mathematical Research)
In this paper, we delve into the study of zero-divisor graphs in rings equipped with an involution. Specifically, we focus on abelian Rickart $*$-rings. Our investigation revolves around characterizing the diameter of a zero-divisor graph in the context of the direct product $\mathcal{S}_1 \oplus \mathcal{S}_2$, in relation to the diameters observed in the zero-divisor graphs of the constituent $*$-rings $\mathcal{S}_1$ and $\mathcal{S}_2$.