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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1241,
author = {T. Tamizh Chelvam and K. Selvakumar},
title = {On the connectivity of the annihilating-ideal graphs},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {35},
year = {2015},
pages = {195-204},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1241}
}
T. Tamizh Chelvam; K. Selvakumar. On the connectivity of the annihilating-ideal graphs. Discussiones Mathematicae - General Algebra and Applications, Tome 35 (2015) pp. 195-204. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1241/
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