Lisa Demeyer

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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.  2004 Elsevier Inc. All rights reserved. This(More)
Given a commutative semigroup S with 0, where 0 is the unique singleton ideal, we associate a simple graph Γ(S), whose vertices are labeled with the nonzero elements in S. Two vertices in Γ(S) are adjacent if and only if the corresponding elements multiply to 0. The inverse problem, i.e., given an arbitrary simple graph, whether or not it can be associated(More)
Let S be a commutative semigroup with zero. The zero divisor graph associated to S, denoted Γ(S) is the graph whose vertices are the nonzero zero divisors of S and two vertices are adjacent in case their product in the semigroup is zero. There are many known results on the possible shape of such graphs. We study the converse problem. Namely, given a graph G(More)
The zero-divisor graph of a commutative semigroup with zero is the graph whose vertices are the nonzero zero-divisors of the semigroup, with two distinct vertices adjacent if the product of the corresponding elements is zero. New criteria to identify zerodivisor graphs are derived using both graph-theoretic and algebraic methods. We find the lowest bound on(More)
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