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On the connectivity of the annihilating-ideal graphs

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Chelvam T., Selvakumar K.

Discussiones Mathematicae - General Algebra and Applications

2015

tom 35

nr 2

195-204

Let R be a commutative ring with identity and 𝔸*(R) the set of non-zero ideals with non-zero annihilators. The annihilating-ideal graph of R is defined as the graph 𝔸𝔾(R) with the vertex set 𝔸*(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.

Ograniczanie wyników

1 Discussiones Mathematicae - General Algebra and Applications

1 Chelvam T.

1 Selvakumar K.

1 2015

Wyniki wyszukiwania

On the connectivity of the annihilating-ideal graphs