The zero-divisor graph of a commutative semigroup

By F. Demeyer, Thomas McKenzie, K. Schneider. 2002

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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.”
Zero divisor graphs of semigroups (2005, background): “5 of [4],a − b is either the edge of a rectangle or triangle in G.”
On Zero Divisor Graphs (2012, background): “R/ is an induced subgraph, note that if there is an edge between Œ'.r1/ and Œ'.r2/ in E .”
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]).”
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].”
An Ideal-Based Zero-Divisor Graph of a Commutative Ring (2003, background): “The zero-divisor graph has been extended to other algebraic structures in DeMeyer et al. (2002) and Redmond (2002).”
Zero-divisor graphs, von Neumann regular rings, and Boolean algebras (2003, background): “The zero-divisor graph of a commutative ring has also been studied in [5,3,9,18,19], and the zero-divisor graph concept has recently been extended to noncommutative rings in [22] and commutative semigroups in [8].”