Author

# A. Parmar

Bio: A. Parmar is an academic researcher from Saurashtra University. The author has contributed to research in topics: Vertex separator & Regular graph. The author has an hindex of 1, co-authored 1 publications receiving 1 citations.

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01 Nov 2015

TL;DR: In this article, the authors considered commutative rings with identity that admit at least two nonzero annihilating ideals and a cut vertex in a ring. And they classified rings such that the complement of a ring is connected and admits at least one cut vertex.

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.

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