Involve: A Journal of Mathematics

  • Involve
  • Volume 11, Number 2 (2018), 283-295.

Zero divisor graphs of commutative graded rings

Katherine Cooper and Brian Johnson

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We study a natural generalization of the zero divisor graph introduced by Anderson and Livingston to commutative rings graded by abelian groups, considering only homogeneous zero divisors. We develop a basic theory for graded zero divisor graphs and present many examples. Finally, we examine classes of graphs that are realizable as graded zero divisor graphs and close with some open questions.

Article information

Involve, Volume 11, Number 2 (2018), 283-295.

Received: 30 September 2016
Revised: 17 March 2017
Accepted: 23 March 2017
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65] 13A02: Graded rings [See also 16W50]

graded ring zero divisor graph


Cooper, Katherine; Johnson, Brian. Zero divisor graphs of commutative graded rings. Involve 11 (2018), no. 2, 283--295. doi:10.2140/involve.2018.11.283.

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