Geodesic
On the connectivity of the annihilating-ideal graphs
Discussiones Mathematicae. General Algebra and Applications, Tome 35 (2015) no. 2, pp. 195-204

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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.
Keywords: annihilating-ideal graph, local ring, nilpotency, cut vertex 
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Chelvam, T.; Selvakumar, K. On the connectivity of the annihilating-ideal graphs. Discussiones Mathematicae. General Algebra and Applications, Tome 35 (2015) no. 2, pp. 195-204. http://geodesic.mathdoc.fr/item/DMGAA_2015_35_2_a5/