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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