On the connectivity of the annihilating-ideal graphs

Let R be a commutative ring with identity and *(R) the set of non-zero ideals with non-zero annihilators. The annihilating-ideal graph of R is defined as the graph (R) with the vertex set *(R) and two distinct vertices I₁ and I₂ are adjacent if and only if I₁I₂ = (0). In this paper, we examine the presence of cut vertices and cut sets in the annihilating-ideal graph of a commutative Artinian ring and provide a partial classification of the rings in which they appear. Using this, we obtain the vertex connectivity of some annihilating-ideal graphs.