Let G=(V,E) be a simple graph. A set SβV is independent set of
G, if no two vertices of S are adjacent. The independence number
Ξ±(G) is the size of a maximum independent set in the graph. %An
independent set with cardinality Let R be a commutative ring with nonzero
identity and I an ideal of R. The zero-divisor graph of R, denoted by
Ξ(R), is an undirected graph whose vertices are the nonzero
zero-divisors of R and two distinct vertices x and y are adjacent if and
only if xy=0. Also the ideal-based zero-divisor graph of R, denoted by
ΞIβ(R), is the graph which vertices are the set {x\in R\backslash I |
xy\in I \quad for some \quad y\in R\backslash I\} and two distinct vertices
x and y are adjacent if and only if xyβI. In this paper we study the
independent sets and the independence number of Ξ(R) and ΞIβ(R).Comment: 27 pages. 22 figure