On a spanning subgraph of the annihilating-ideal graph of a commutative ring.

The rings considered in this paper are commutative with identity which are not integral domains. Let R be a ring. Let us denote the set of all annihilating ideals of R by (R) and (R) ∖ { (0) } by (R) ∗ . With R , we associate an undirected graph, denoted by (R) , whose vertex set is (R) ∗ and distinct vertices I and J are adjacent in this graph if and only if I J = (0) and I + J ∈ (R). The aim of this paper is to study the interplay between the graph-theoretic properties of (R) and the ring-theoretic properties of  R. [ABSTRACT FROM AUTHOR]