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.