A Graphical Characterization for SPAP-Rings

Let R be a commutative ring and I an ideal of R. The zero-divisor graph of R with respect to I, denoted by ΓI (R), is the simple graph whose vertex set is {x ∈ R \ I | xy ∈ I, for some y ∈ R \ I}, with two distinct vertices x and y are adjacent if and only if xy ∈ I. In this paper, we state a relation between zero-divisor graph of R with respect to an ideal and almost prime ideals of R. We then use this result to give a graphical characterization for SPAP -rings.