Some properties of the zero divisor graph of a commutative ring

Khalida Nazzal; Manal Ghanem

Discussiones Mathematicae - General Algebra and Applications (2014)

  • Volume: 34, Issue: 2, page 167-181
  • ISSN: 1509-9415

Abstract

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Let Γ(R) be the zero divisor graph for a commutative ring with identity. The k-domination number and the 2-packing number of Γ(R), where R is an Artinian ring, are computed. k-dominating sets and 2-packing sets for the zero divisor graph of the ring of Gaussian integers modulo n, Γ(ℤₙ[i]), are constructed. The center, the median, the core, as well as the automorphism group of Γ(ℤₙ[i]) are determined. Perfect zero divisor graphs Γ(R) are investigated.

How to cite

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Khalida Nazzal, and Manal Ghanem. "Some properties of the zero divisor graph of a commutative ring." Discussiones Mathematicae - General Algebra and Applications 34.2 (2014): 167-181. <http://eudml.org/doc/270207>.

@article{KhalidaNazzal2014,
abstract = {Let Γ(R) be the zero divisor graph for a commutative ring with identity. The k-domination number and the 2-packing number of Γ(R), where R is an Artinian ring, are computed. k-dominating sets and 2-packing sets for the zero divisor graph of the ring of Gaussian integers modulo n, Γ(ℤₙ[i]), are constructed. The center, the median, the core, as well as the automorphism group of Γ(ℤₙ[i]) are determined. Perfect zero divisor graphs Γ(R) are investigated.},
author = {Khalida Nazzal, Manal Ghanem},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {automorphism group of a graph; center of a graph; core of a graph; k-domination number; Gaussian integers modulo n; median of a graph; 2-packing; perfect graph; and zero divisor graph; zero divisor graphs of commutative rings},
language = {eng},
number = {2},
pages = {167-181},
title = {Some properties of the zero divisor graph of a commutative ring},
url = {http://eudml.org/doc/270207},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Khalida Nazzal
AU - Manal Ghanem
TI - Some properties of the zero divisor graph of a commutative ring
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2014
VL - 34
IS - 2
SP - 167
EP - 181
AB - Let Γ(R) be the zero divisor graph for a commutative ring with identity. The k-domination number and the 2-packing number of Γ(R), where R is an Artinian ring, are computed. k-dominating sets and 2-packing sets for the zero divisor graph of the ring of Gaussian integers modulo n, Γ(ℤₙ[i]), are constructed. The center, the median, the core, as well as the automorphism group of Γ(ℤₙ[i]) are determined. Perfect zero divisor graphs Γ(R) are investigated.
LA - eng
KW - automorphism group of a graph; center of a graph; core of a graph; k-domination number; Gaussian integers modulo n; median of a graph; 2-packing; perfect graph; and zero divisor graph; zero divisor graphs of commutative rings
UR - http://eudml.org/doc/270207
ER -

References

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