Zero-Divisor Graph with Respect to an Ideal *

  title={Zero-Divisor Graph with Respect to an Ideal *},
  author={Hamid Reza Maimani and M. R. Pournaki},
Let R be a commutative ring with nonzero identity and let I be an ideal of R. The zero-divisor graph of R with respect to I, denoted by ΓI(R), is the graph whose vertices are the set {x ∈ R \ I| xy ∈ I for some y ∈ R \ I} with distinct vertices x and y adjacent if and only if xy ∈ I. In the case I = 0, Γ0(R), denoted by Γ(R), is the zero-divisor graph which… CONTINUE READING