exploring the properties of the zero-divisor graph of direct product of $ast$-rings

In this paper, we delve into the study of zero-divisor graphs in rings equipped with an involution. specifically, we focus on abelian rickart $ast$-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 $ast$-rings $mathcal{s}_1$ and $mathcal{s}_2$.