# On the connectivity of the annihilating-ideal graphs

T. Tamizh Chelvam; K. Selvakumar

Discussiones Mathematicae - General Algebra and Applications (2015)

- Volume: 35, Issue: 2, page 195-204
- ISSN: 1509-9415

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topT. Tamizh Chelvam, and K. Selvakumar. "On the connectivity of the annihilating-ideal graphs." Discussiones Mathematicae - General Algebra and Applications 35.2 (2015): 195-204. <http://eudml.org/doc/276649>.

@article{T2015,

abstract = {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.},

author = {T. Tamizh Chelvam, K. Selvakumar},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {annihilating-ideal graph; local ring; nilpotency; cut vertex},

language = {eng},

number = {2},

pages = {195-204},

title = {On the connectivity of the annihilating-ideal graphs},

url = {http://eudml.org/doc/276649},

volume = {35},

year = {2015},

}

TY - JOUR

AU - T. Tamizh Chelvam

AU - K. Selvakumar

TI - On the connectivity of the annihilating-ideal graphs

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2015

VL - 35

IS - 2

SP - 195

EP - 204

AB - 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.

LA - eng

KW - annihilating-ideal graph; local ring; nilpotency; cut vertex

UR - http://eudml.org/doc/276649

ER -

## References

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