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The zero-divisor graph of a commutative semigroup

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Abstract

An undirected graph Γ(S) is associated to each commutative multiplicative semigroup S with 0. The vertices of the graph are labeled by the nonzero zero-divisors of S , and two vertices x,y are connected by an edge in case xy = 0 in S . The properties and possible structures of the graph Γ (S) are studied.

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Authors and Affiliations

  1. Department of Mathematics, Colorado State University, 80523, Fort Collins, CO

    F. R. DeMeyer

  2. Department of Mathematics, Bradley University, 61625, Peoria, IL

    T. McKenzie

  3. Department of Mathematics, Mesa State University, 81502, Grand Junction, CO

    K. Schneider

Authors
  1. F. R. DeMeyer
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  2. T. McKenzie
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  3. K. Schneider
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Corresponding author

Correspondence to F. R. DeMeyer.

Additional information

Communicated by BorisM. Schein

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DeMeyer, F.R., McKenzie, T. & Schneider, K. The zero-divisor graph of a commutative semigroup. Semigroup Forum 65, 206–214 (2002). https://doi.org/10.1007/s002330010128

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  • DOI: https://doi.org/10.1007/s002330010128

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