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Simple Graphs and Commutative Zero-Divisor Semigroups

Tongsuo Wu·Li Chen
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Abstract

In this paper, we study commutative zero-divisor semigroups determined by graphs. We prove a uniqueness theorem for a class of graphs. We show two classes of graphs that have no corresponding semigroups. In particular, any complete graph $K_n$ together with more than three end vertices and any complete bipartite graph together with more than one end vertices have no corresponding semigroups. We also determine all possible zero-divisor semigroups whose zero-divisor graph is the com- plete graph $K_3$ together with two end vertices.

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Tongsuo Wu, Li Chen. 2005-12-26. Simple Graphs and Commutative Zero-Divisor Semigroups. https://arxiv.org/abs/math/0512567

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