Document Type : Research Paper

**Authors**

Saurashtra University, Rajkot, India

**Abstract**

The rings considered in this article are commutative with identity which admit at least two nonzero annihilating ideals. Let $R$ be a ring. Let $\mathbb{A}(R)$ denote the set of all annihilating ideals of $R$ and let $\mathbb{A}(R)^{*} = \mathbb{A}(R)\backslash \{(0)\}$. The annihilating-ideal graph of $R$, denoted by $\mathbb{AG}(R)$ is an undirected simple graph whose vertex set is $\mathbb{A}(R)^{*}$ 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 $(\mathbb{AG}(R))^{c}$ ( that is, the complement of $\mathbb{AG}(R)$) is connected and admits a cut vertex.

**Keywords**

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November 2015

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