Abstract
Zero-divisor graphs of rings have been developed and explored by D. F. Anderson and Livingston, Redmond, and others ([4], [5], [15], [17]). Additionally, these ideas have been adapted to semigroups by DeMeyer, McKenzie, and Schneider [10]. Results concerning the properties of graphs of semigroups are presented. All possible zero-divisor graphs of nearrings with identity in which the graph has less than five vertices are classified, and the additive group of each nonring is identified. Following the example of [7], we include a table of nearrings with identity of orders between sixteen and thirty-one.
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Cannon, G.A., Neuerburg, K.M., Redmond, S.P. (2005). Zero-Divisor Graphs of Nearrings and Semigroups. In: Kiechle, H., Kreuzer, A., Thomsen, M.J. (eds) Nearrings and Nearfields. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3391-5_8
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DOI: https://doi.org/10.1007/1-4020-3391-5_8
Publisher Name: Springer, Dordrecht
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