When does the complement of the annihilating-ideal graph of a commutative ring admit a cut vertex?

The rings considered in this article are commutative with identity which admit at least two nonzero annihilating ideals. Let R be a ring. Let A(R) denote the set of all annihilating ideals of R and let A(R)∗=A(R)∖{(0)}. The annihilating-ideal graph of R, denoted by AG(R) is an undirected simple graph whose vertex set is A(R)∗ and distinct vertices I,J are joined by an edge in this graph if and only if IJ=(0). The aim of this article is to classify rings R such that (AG(R))c ( that is, the complement of AG(R)) is connected and admits a cut vertex.