Zero divisor graphs of semigroups

By F. Demeyer, Lisa Demeyer. 2005

177 citations recorded by the source corpus.

The zero divisor graph of a commutative semigroup with zero is a graph whose vertices are the nonzero zero divisors of the semigroup, with two distinct vertices joined by an edge in case their product in the semigroup is zero. We continue the study of this construction and its extension to a simplicial complex.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b4aff45b9fd65fda497b5a0fbebad0aa570bd16a

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In Algebra and Number Theory

In Geometry and Topology

Citations in the corpus

A Zero Divisor Graph Determined by Equivalence Classes of Zero Divisors (2007, background): “The zero divisor graph of such semigroups have been studied extensively, beginning with [7] and continuing in [6] among many others.”
Commutative Boolean monoids, reduced rings, and the compressed zero-divisor graph (2012, background): “The generalization of zero-divisor graphs to semigroupswas initiated in [12], and has been continued in [11,14].”
On Zero Divisor Graphs (2012, unknown): “Authenticated | sean.sather-wagstaff@ndsu.edu author's copy Download Date | 5/22/12 4:06 PM Proposition 4.2.”
The Annihilating-Ideal Graph of Commutative Rings I (2008, background): “In the literature, there are many papers on assigning a graph to a ring, a group, semigroup or a module (see, for example, [1–11, 14–18]).”