independent sets of some graphs associated to commutative rings

Let g=(v,e)g=(v,e) be a simple graph. a set s⊆vs⊆v is independent set of gg, if no two vertices of ss are adjacent. the independence number α(g)α(g) is the size of a maximum independent set in the graph. in this paper we study and characterize the independent sets of the zero-divisor graph γ(r)γ(r) and ideal-based zero-divisor graph γi(r)γi(r) of a commutative ring rr.